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ANSI B92.1-1970 SAE花键标准|花​键​标​准
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你可能喜欢INVOLUTE SPLINES2129Form Circle is the circle which defines the deepest points of involute form control of the tooth profile. This circle along with the tooth tip circle (or start of chamfer circle) determines the limits of tooth profile requiring control. It is located near the major circle on the internal spline and near the minor circle on the external spline. Form Clearance (cF) is the radial depth of involute profile beyond the depth of engagement with the mating part. It allows for looseness between mating splines and for eccentricities between the minor circle (internal), the major circle (external), and their respective pitch circles. Form Diameter (DFe, DFi) the diameter of the form circle. Internal Spline is a spline formed on the inner surface of a cylinder. Involute Spline is one having teeth with involute profiles. Lead Variation is the variation of the direction of the spline tooth from its intended direction parallel to the reference axis, also including parallelism and alignment variations (see Fig. 1a). Note: Straight (nonhelical) splines have an infinite lead. Length of Engagement (Lq) is the axial length of contact between mating splines. Machining Tolerance (m) is the permissible variation in actual space width or actual tooth thickness. Major Circle is the circle formed by the outermost surface of the spline. It is the outside circle (tooth tip circle) of the external spline or the root circle of the internal spline. Major Diameter (Do, Dri) is the diameter of the major circle. Minor Circle is the circle formed by the innermost surface of the spline. It is the root circle of the external spline or the inside circle (tooth tip circle) of the internal spline. Minor Diameter (Dre, Di) is the diameter of the minor circle. Nominal Clearance is the actual space width of an internal spline minus the actual tooth thickness of the mating external spline. It does not define the fit between mating members, because of the effect of variations. Out of Roundness is the variation of the spline from a true circular configuration. Parallelism Variation is the variation of parallelism of a single spline tooth with respect to any other single spline tooth (see Fig. 1b). Pitch (P/Ps) is a combination number of a one-to-two ratio indicating th the upper or first number is the diametral pitch, the lower or second number is the stub pitch and denotes, as that fractional part of an inch, the basic radial length of engagement, both above and below the pitch circle. Pitch Circle is the reference circle from which all transverse spline tooth dimensions are constructed. Pitch Diameter (D) is the diameter of the pitch circle. Pitch Point is the intersection of the spline tooth profile with the pitch circle. Pressure Angle (φ) is the angle between a line tangent to an involute and a radial line through the point of tangency. Unless otherwise specified, it is the standard pressure angle. Profile Variation is any variation from the specified tooth profile normal to the flank. Spline is a machine element consisting of integral keys (spline teeth) or keyways (spaces) equally spaced around a circle or portion thereof. Standard (Main) Pressure Angle (φD) is the pressure angle at the specified pitch diameter. Stub Pitch (Ps) is a number used to denote the radial distance from the pitch circle to the major circle of the external spline and from the pitch circle to the minor circleof the internal spline. The stub pitch for splines in this standard is twice the diametral pitch. Total Index Variation is the greatest difference in any two teeth (adjacent or otherwise) between the actual and the perfect spacing of the tooth profiles. Total Tolerance (m + λ) is the machining tolerance plus the variation allowance. Variation Allowance (λ) is the permissible effective variation.2130INVOLUTE SPLINESTooth Proportions.—There are 17 pitches: 2.5 ?5, 3?6, 4?8,5?10, 6?12, 8?16, 10?20, 12?24, 16?32, 20?40, 24?48, 32?64, 40?80, 48?96, 64?128, 80?160, and 128?256. The numerator in this fractional designation is known as the diametral pitch and control the denominator, which is always double the numerator, is known as the stub pitch and controls the tooth depth. For convenience in calculation, only the numerator is used in the formulas given and is designated as P. Diametral pitch, as in gears, means the number of teeth per inch of pitch diameter. Table 1 shows the symbols and Table 2 the formulas for basic tooth dimensions of involute spline teeth of various pitches. Basic dimensions are given in Table 3. Table 1. American National Standard Involute Spline Symbols ANSI B92.1-1970, R1993cv cF D Db Dci Dce DFe DFi Di Do Dre Dri de di Ke Ki L La Lg m Me effective clearance form clearance pitch diameter base diameter pin contact diameter, internal spline pin contact diameter, external spline form diameter, external spline form diameter, internal spline minor diameter, internal spline major diameter, external spline minor diameter, external spline (root) major diameter, internal spline (root) diameter of measuring pin for external spline diameter of measuring pin for internal spline change factor for external spline change factor for internal spline spline length active spline length length of engagement machining tolerance measurement over pins, external spline Mi N P Ps p rf s sv sc ss t tv λ ∈ φ φD φci φce φi φe φF measurement between pins, internal spline number of teeth diametral pitch stub pitch circular pitch fillet radius actual space width, circular effective space width, circular allowable compressive stress, psi allowable shear stress, psi actual tooth thickness, circular effective tooth thickness, circular variation allowance involute roll angle pressure angle standard pressure angle pressure angle at pin contact diameter, internal spline pressure angle at pin contact diameter, external spline pressure angle at pin center, internal spline pressure angle at pin center, external spline pressure angle at form diameterTable 2. Formulas for Basic Dimensions ANSI B92.1-1970, R1993Formula 30 deg φD Term Symbol Flat Root Side Fit 2.5?5–32?64 Pitch Stub Pitch Pitch Diameter Base Diameter Circular Pitch Minimum Effective Space Width Major Diameter, Internal Major Diameter, External Minor Diameter, Internal Ps D Db p 2P Flat Root Major Dia Fit 3?6–16?32 Pitch 2P Fillet Root Side Fit 2.5?5–48?96 Pitch 2P Fillet Root Side Fit 2.5?5–48?96 Pitch 2P Fillet Root Side Fit 10?20–128?256 Pitch 2P 37.5 deg φD 45 deg φDN --PD cos φDN --PD cos φDN --PD cos φDN --PD cos φDN --PD cos φDINVOLUTE SPLINESπ -P π -----2P N + 1.35 -------------------P N+1 -----------P N–1 -----------Pπ -P π -----2P N+1 -----------P N+1 -----------P N–1 -----------Pπ -P π -----2P N + 1.8 ----------------P N+1 -----------P N–1 -----------Pπ -P 0.5π + 0.1 -----------------------P N + 1.6 ----------------P N+1 -----------P N – 0.8 ---------------Pπ -P 0.5π + 0.2 -----------------------P N + 1.4 ----------------P N+1 -----------P N – 0.6 ---------------PsvDriDoDi2131Table 2. (Continued) Formulas for Basic Dimensions ANSI B92.1-1970, R1993Formula 30 deg φD Term Symbol Flat Root Side Fit 2.5?5–32?64 Pitch 2.5?5 thru 12?24 pitch Minor Dia. Ext. 16?32 pitch and finer 10?20 16?32 pitch and finer Form Diameter, Internal Form Diameter, External Form Clearance (Radial) DFi Flat Root Major Dia Fit 3?6–16?32 Pitch Fillet Root Side Fit 2.5?5–48?96 Pitch Fillet Root Side Fit 2.5?5–48?96 Pitch Fillet Root Side Fit 10?20–128?256 Pitch 37.5 deg φD 45 deg φD2132N – 1.8 ---------------P… DreINVOLUTE SPLINESN – 1.35 ------------------PN–2 -----------P…N – 1.3 ---------------P N–1 -----------P N+1 ------------ + 2cF P N – 0.8 ---------------- – 2cF P N+1 ------------ + 2cF P N – 0.6 ---------------- – 2cF PN+1 ------------ + 2cF P N–1 ------------ – 2cF PN + 0.8 ----------------- – 0.004 + 2cF P N–1 ------------ – 2cF PN+1 ------------ + 2cF P N–1 ------------ – 2cF PDFecF0.001 D, with max of 0.010, min of 0.002π = 3.1415927 Note: All spline specification table dimensions in the standard are derived from these basic formulas by application of tolerances.INVOLUTE SPLINESTable 3. Basic Dimensions for Involute Splines ANSI B92.1-1970, R1993Pitch, P/Ps 2.5?5 3?6 4?8 5?10 6?12 8?16 10?20 12?24 16?32 Circular Pitch, p 1.2 0.3 0.7 0.8 0.1963 Min Effective Space Width (BASIC), Sv min 30 deg φ 37.5 deg φ 45 deg φ 0.3 … 0.7 0.8 0.1 0.2 0.7 0.5 0.1 0.4 … … … … … 0.6 0.1107 Pitch, P/Ps 20?40 24?48 32?64 40?80 48?96 64?128 80?160 128?256 … Circular Pitch, p 0.9 0.5 0.1 0.6 …2133Min Effective Space Width (BASIC), Sv min 30 deg φ 37.5 deg φ 45 deg φ 0.5 0.4 0.3 0.0327 … … … … 0.2 0.8 … … … … 0.3 0.9 0.1 0.0138 …Tooth Numbers.—The American National Standard covers involute splines having tooth numbers ranging from 6 to 60 with a 30- or 37.5-degree pressure angle and from 6 to 100 with a 45-degree pressure angle. In selecting the number of teeth for a given spline application, it is well to keep in mind that there are no advantages to be gained by using odd numbers of teeth and that the diameters of splines with odd tooth numbers, particularly internal splines, are troublesome to measure with pins since no two tooth spaces are diametrically opposite each other. Types and Classes of Involute Spline Fits.—Two types of fits are covered by the American National Standard for involute splines, the side fit, and the major diameter fit. Dimensional data for flat root side fit, flat root major diameter fit, and fillet root side fit splines are tabulated in this standard for 30-degree pr but for only the fillet root side fit for 37.5- and 45-degree pressure angle splines. Side Fit: In the side fit, the mating members contact only on th major and minor diameters are clearance dimensions. The tooth sides act as drivers and centralize the mating splines. Major Diameter Fit: Mating parts for this fit contact at the major diameter for centralizing. The sides of the teeth act as drivers. The minor diameters are clearance dimensions. The major diameter fit provides a minimum effective clearance that will allow for contact and location at the major diameter with a minimum amount of location or centralizing effect by the sides of the teeth. The major diameter fit has only one space width and tooth thickness tolerance which is the same as side fit Class 5. A fillet root may be specified for an external spline, even though it is otherwise designed to the flat root side fit or major diameter fit standard. An internal spline with a fillet root can be used only for the side fit. Classes of Tolerances.—This standard includes four classes of tolerances on space width and tooth thickness. This has been done to provide a range of tolerances for selection to suit a design need. The classes are variations of the former single tolerance which is now Class 5 and are based on the formulas shown in the footnote of Table 4. All tolerance classes have the same minimum effective space width and maximum effective tooth thickness limits so that a mix of classes between mating parts is possible.2134INVOLUTE SPLINESTable 4. Maximum Tolerances for Space Width and Tooth Thickness of Tolerance Class 5 Splines ANSI B92.1-1970, R1993 (Values show 20 = 0.0020)No. of Teeth N 10 20 30 40 50 60 70 80 90 100 N 10 20 30 40 50 60 70 80 90 100 N 10 20 30 40 50 60 70 80 90 100 N All +7 ?10 +6 ?8 +5 ?7 20 24 28 32 36 40 — — — — 17 20 22 25 27 30 — — — — 15 18 20 22 25 27 — — — — 23.5 27.0 30.5 34.0 37.5 41.0 — — — — 20.3 22.6 24.9 27.2 29.5 31.8 — — — — 17.0 19.0 21.0 23.0 25.0 27.0 — — — — 15.8 17.6 18.4 21.8 23.0 24.8 — — — — 14.5 16.0 17.5 19.0 20.5 22.0 — — — — 12.5 14.0 15.5 17.0 18.5 20.0 — — — — Pitch, P/Ps 2.5?5 and 3?6 4?8 and 5?10 6?12 and 8?16 10?20 and 12?24 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0 21.0 15.7 17.4 19.1 21.6 22.5 24.2 25.9 27.6 29.3 31.0 15 17 19 20 22 24 26 28 29 31 +4 ?6 Lead Variation Lg, in. Variation 0.3 2 0.5 3 1 4 2 5 3 6 4 7 5 8 6 9 7 10 8 11 9 12 10 13 16?32 and 20?40 11.7 12.4 13.1 13.8 14.5 15.2 15.9 16.6 17.3 18.0 14.2 15.4 16.6 17.8 19.0 20.2 21.4 22.6 23.8 25.0 14 15 16 18 19 20 21 22 24 25 +3 ?5 24?48 thru 48?96 11.7 12.4 13.1 13.8 14.5 15.2 15.9 16.6 17.3 18.0 12.2 13.4 14.6 15.8 17.0 18.2 19.4 20.6 21.8 23.0 12 13 15 16 17 18 20 21 23 24 +2 ?4 64?128 and 80?160 9.6 10.2 10.8 11.4 — — — — — — 11.0 12.0 13.0 14.0 — — — — — — 11 12 14 15 — — — — — — +2 ?4 128?256Machining Tolerance, m 9.5 10.0 10.5 — — — — — — — 9.8 10.6 11.4 — — — — — — — 10 11 13 — — — — — — — +2 ?4Variation Allowance, λTotal Index VariationProfile VariationFor other tolerance classes: Class 4 = 0.71 × Tabulated value Class 5 = As tabulated in table Class 6 = 1.40 × Tabulated value Class 7 = 2.00 × Tabulated valueINVOLUTE SPLINES2135Fillets and Chamfers.—Spline teeth may have either a flat root or a rounded fillet root. Flat Root Splines: are suitable for most applications. The fillet that joins the sides to the bottom of the tooth space, if generated, has a varying radius of curvature. Specification of this fillet is usually not required. It is controlled by the form diameter, which is the diameter at the deepest point of the desired true involute form (sometimes designated as TIF). When flat root splines are used for heavily loaded couplings that are not suitable for fillet root spline application, it may be desirable to minimize the stress concentration in the flat root type by specifying an approximate radius for the fillet. Because internal splines are stronger than external splines due to their broad bases and high pressure angles at the major diameter, broaches for flat root internal splines are normally made with the involute profile extending to the major diameter. Fillet Root Splines: are recommended for heavy loads because the larger fillets provided reduce the stress concentrations. The curvature along any generated fillet varies and cannot be specified by a radius of any given value. External splines may be produced by generating with a pinion-type shaper cutter or with a hob, or by cutting with no generating motion using a tool formed to the contour of a tooth space. External splines are also made by cold forming and are usually of the fillet root design. Internal splines are usually produced by broaching, by form cutting, or by generating with a shaper cutter. Even when full-tip radius tools are used, each of these cutting methods produces a fillet contour with individual characteristics. Generated spline fillets are curves related to the prolate epicycloid for external splines and the prolate hypocycloid for internal splines. These fillets have a minimum radius of curvature at the point where the fillet is tangent to the external spline minor diameter circle or the internal spline major diameter circle and a rapidly increasing radius of curvature up to the point where the fillet comes tangent to the involute profile. Chamfers and Corner Clearance: In major diameter fits, it is always necessary to provide corner clearance at the major diameter of the spline coupling. This clearance is usually effected by providing a chamfer on the top corners of the external member. This method may not be possible or feasible because of the following: A) If the external member is roll formed by plastic deformation, a chamfer cannot be provided by the process. B) A semitopping cutter may not be available. C) When cutting external splines with small numbers of teeth, a semitopping cutter may reduce the width of the top land to a prohibitive point. In such conditions, the corner clearance can be provided on the internal spline, as shown in Fig. 2. When this option is used, the form diameter may fall in the protuberance area.0.120 min P 0.200 max PFig. 2. Internal corner clearance.Spline Variations.—The maximum allowable variations for involute splines are listed in Table 4.2136INVOLUTE SPLINESProfile Variation: The reference profile, from which variations occur, passes through the point used to determine the actual space width or tooth thickness. This is either the pitch point or the contact point of the standard measuring pins. Profile variation is positive in the direction of the space and negative in the direction of the tooth. Profile variations may occur at any point on the profile for establishing effective fits and are shown in Table 4. Lead Variations: The lead tolerance for the total spline length applies also to any portion thereof unless otherwise specified. Out of Roundness: This condition may appear merely as a result of index and profile variations given in Table 4 and requires no further allowance. However, heat treatment and deflection of thin sections may cause out of roundness, which increases index and profile variations. Tolerances for such conditions depend on many variables and are therefore not tabulated. Additional tooth and/or space width tolerance must allow for such conditions. Eccentricity: Eccentricity of major and minor diameters in relation to the effective diameter of side fit splines should not cause contact beyond the form diameters of the mating splines, even under conditions of maximum effective clearance. This standard does not establish specific tolerances. Eccentricity of major diameters in relation to the effective diameters of major diameter fit splines should be absorbed within the maximum material limits established by the tolerances on major diameter and effective space width or effective tooth thickness. If the alignment of mating splines is affected by eccentricity of locating surfaces relative to each other and/or the splines, it may be necessary to decrease the effective and actual tooth thickness of the external splines in order to maintain the desired fit condition. This standard does not include allowances for eccentric location. Effect of Spline Variations.—Spline variations can be classified as index variations, profile variations, or lead variations. Index Variations: These variations cause the clearance to vary from one set of mating tooth sides to another. Because the fit depends on the areas with minimum clearance, index variations reduce the effective clearance. Profile Variations: Positive profile variations affect the fit by reducing effective clearance. Negative profile variations do not affect the fit but reduce the contact area. Lead Variations: These variations will cause clearance variations and therefore reduce the effective clearance. Variation Allowance: The effect of individual spline variations on the fit (effective variation) is less than their total, because areas of more than minimum clearance can be altered without changing the fit. The variation allowance is 60 percent of the sum of twice the positive profile variation, the total index variation and the lead variation for the length of engagement. The variation allowances in Table 4 are based on a lead variation for an assumed length of engagement equal to one-half the pitch diameter. Adjustment may be required for a greater length of engagement. Effective and Actual Dimensions.—Although each space of an internal spline may have the same width as each tooth of a perfect mating external spline, the two may not fit because of variations of index and profile in the internal spline. To allow the perfect external spline to fit in any position, all spaces of the internal spline must then be widened by the amount of interference. The resulting width of these tooth spaces is the actual space width of the internal spline. The effective space width is the tooth thickness of the perfect mating external spline. The same reasoning applied to an external spline that has variations of index and profile when mated with a perfect internal spline leads to the concept of effective tooth thickness, which exceeds the actual tooth thickness by the amount of the effective variation.INVOLUTE SPLINES2137The effective space width of the internal spline minus the effective tooth thickness of the external spline is the effective clearance and defines the fit of the mating parts. (This statement is strictly true only if high points of mating parts come into contact.) Positive effective clearance represents looseness or backlash. Negative effective clearance represents tightness or interference. Space Width and Tooth Thickness Limits.—The variation of actual space width and actual tooth thickness within the machining tolerance causes corresponding variations of effective dimensions, so that there are four limit dimensions for each component part. These variations are shown diagrammatically in Table 5. Table 5. Specification Guide for Space Width and Tooth Thickness ANSI B92.1-1970, R1993The minimum effective space width is always basic. The maximum effective tooth thickness is the same as the minimum effective space width except for the major diameter fit. The major diameter fit maximum effective tooth thickness is less than the minimum effective space width by an amount that allows for eccentricity between the effective spline and the major diameter. The permissible variation of the effective clearance is divided between the internal and external splines to arrive at the maximum effective space width and the minimum effective tooth thickness. Limits for the actual space width and actual tooth thickness are constructed from suitable variation allowances. Use of Effective and Actual Dimensions.—Each of the four dimensions for space width and tooth thickness shown in Table 5 has a definite function. Minimum Effective Space Width and Maximum Effective Tooth Thickness: T h e s e dimensions control the minimum effective clearance, and must always be specified. Minimum Actual Space Width and Maximum Actual Tooth Thickness: T h e s e d i m e n sions cannot be used for acceptance or rejection of parts. If the actual space width is less than the minimum without causing the effective space width to be undersized, or if the actual tooth thickness is more than the maximum without causing the effective tooth thickness to be oversized, the effective variation is l such parts are desirable and not defective. The specification of these dimensions as processing reference dimensions is optional. They are also used to analyze undersize effective space width or oversize effective tooth thickness conditions to determine whether or not these conditions are caused by excessive effective variation. Maximum Actual Space Width and Minimum Actual Tooth Thickness: T h e s e d i m e n sions control machining tolerance and limit the effective variation. The spread between these dimensions, reduced by the effective variation of the internal and external spline, is2138INVOLUTE SPLINESthe maximum effective clearance. Where the effective variation obtained in machining is appreciably less than the variation allowance, these dimensions must be adjusted in order to maintain the desired fit. Maximum Effective Space Width and Minimum Effective Tooth Thickness: T h e s e dimensions define the maximum effective clearance but they do not limit the effective variation. They may be used, in addition to the maximum actual space width and minimum actual tooth thickness, to prevent the increase of maximum effective clearance due to reduction of effective variations. The notation “inspection optional” may be added where maximum effective clearance is an assembly requirement, but does not need absolute control. It will indicate, without necessarily adding inspection time and equipment, that the actual space width of the internal spline must be held below the maximum, or the actual tooth thickness of the external spline above the minimum, if machining methods result in less than the allowable variations. Where effective variation needs no control or is controlled by laboratory inspection, these limits may be substituted for maximum actual space width and minimum actual tooth thickness. Combinations of Involute Spline Types.—Flat root side fit internal splines may be used with fillet root external splines where the larger radius is desired on the external spline for control of stress concentrations. This combination of fits may also be permitted as a design option by specifying for the minimum root diameter of the external, the value of the minimum root diameter of the fillet root external spline and noting this as “optional root.” A design option may also be permitted to provide either flat root internal or fillet root internal by specifying for the maximum major diameter, the value of the maximum major diameter of the fillet root internal spline and noting this as “optional root.” Interchangeability.—Splines made to this standard may interchange with splines made to older standards. Exceptions are listed below. External Splines: These external splines will mate with older internal splines as follows: Year b
SAE 1960b Full dedendum. c Short dedendum.Major Dia. Fit Yes Yes (B) Yes (B) Yes YesFlat Root Side Fit No (A)a Yes (B) No (A) No (A) No (A)Fillet Root Side Fit No (A) Yes (C) Yes (C) Yes (C) Yes (C)a For exceptions A, B, C, see the paragraph on Exceptions that follows.Internal Splines: These will mate with older external splines as follows: Year 57 SAE 1960 Major Dia. Fit No (D)a Yes (F) Yes (G) Yes (G) Flat Root Side Fit No (E) Yes Yes Yes Fillet Root Side Fit No (D) Yes (C) Yes Yesa For exceptions C, D, E, F, G, see the paragraph on Exceptions that follows.INVOLUTE SPLINES2139Table 6. Spline Terms, Symbols, and Drawing Data, 30-Degree Pressure Angle, Flat Root Side Fit ANSI B92.1-1970, R199330-Deg Pressure Angle Space Width (Circular) s = Actual sv = Effective Tooth Thickness (Circular) t = Actual tv = Effective Circular Pitch P Fillet Form Clearance CInternal SplineFOptional Pitch Dia. D RefExternal SplineMajor Dia. Do DriCF Major Dia. Di Dre Major Dia. DFe DFiThe fit shown is used in restricted areas (as with tubular parts with wall thickness too small to permit use of fillet roots, and to allow hobbing closer to shoulders, etc.) and for economy (when hobbing, shaping, etc., and using shorter broaches for the internal member). Press fits are not tabulated because their design depends on the degree of tightness desired and must allow for such factors as the shape of the blank, wall thickness, materila, hardness, thermal expansion, etc. Close tolerances or selective size grouping may be required to limit fit variations. Drawing Data Internal Involute Spline Data Flat Root Side Fit Number of Teeth Pitch Pressure Angle Base Diameter Pitch Diameter Major Diameter Form Diameter Minor Diameter Circular Space Width Max Min Actual Effective x.xxxx x.xxxx xx xx/xx 30° x.xxxxxx Ref x.xxxxxx Ref x.xxx max x.xxx x.xxx/x.xxx External Involute Spline Data Flat Root Side Fit Number of Teeth Pitch Pressure Angle Base Diameter Pitch Diameter Major Diameter Form Diameter Minor Diameter Circular Tooth Thickness Max Min Effective Actual x.xxxx x.xxxx xx xx/xx 30° x.xxxxxx Ref x.xxxxxx Ref x.xxx/x.xxx x.xxx x.xxx minThe following information may be added as required: Max Measurement Between Pins Pin Diameter x.xxx Ref x.xxxxThe following information may be added as required: Min Measurement Over Pins Pin Diameter x.xxxx Ref x.xxxxThe above drawing data are required for the spline specifications. The stan for alternate systems, see Table 5. Number of x's indicates number of decimal places normally used.2140INVOLUTE SPLINESExceptions: A) The external major diameter, unless chamfered or reduced, may interfere with the internal form diameter on flat root side fit splines. Internal splines made to the 1957 and 1960 standards had the same dimensions as shown for the major diameter fit splines in this standard. B) For 15 teeth or less, the minor diameter of the internal spline, unless chamfered, will interfere with the form diameter of the external spline. C) For 9 teeth or less, the minor diameter of the internal spline, unless chamfered, will interfere with form diameter of the external spline. D) The internal minor diameter, unless chamfered, will interfere with the external form diameter. E) The internal minor diameter, unless chamfered, will interfere with the external form diameter. F) For 10 teeth or less, the minimum chamfer on the major diameter of the external spline may not clear the internal form diameter. G) Depending upon the pitch of the spline, the minimum chamfer on the major diameter may not clear the internal form diameter. Drawing Data.—It is important that uniform specifications be used to show complete information on detail drawings of splines. Much misunderstanding will be avoided by following the suggested arrangement of dimensions and data as given in Table 6. The number of x's indicates the number of decimal places normally used. With this tabulated type of spline specifications, it is usually not necessary to show a graphic illustration of the spline teeth. Spline Data and Reference Dimensions.—Spline data are used for engineering and manufacturing purposes. Pitch and pressure angle are not subject to individual inspection. As used in this standard, reference is an added notation or modifier to a dimension, specification, or note when that dimension, specification, or note is: 1) Repeated for drawing clarification. 2) Needed to define a nonfeature datum or basis from which a form or feature is generated. 3) Needed to define a nonfeature dimension from which other specifications or dimensions are developed. 4) Needed to define a nonfeature dimension at which toleranced sizes of a feature are specified. 5) Needed to define a nonfeature dimension from which control tolerances or sizes are developed or added as useful information. Any dimension, specification, or note that is noted “REF” should not be used as a criterion for part acceptance or rejection. Estimating Key and Spline Sizes and Lengths.—Fig. 1 may be used to estimate the size of American Standard involute splines required to transmit a given torque. It also may be used to find the outside diameter of shafts used with single keys. After the size of the shaft is found, the proportions of the key can be determined from Table 1 on page 2342. Curve A is for flexible splines with teeth hardened to Rockwell C 55–65. For these splines, lengths are generally made equal to or somewhat greater than the pitch diameter for diameters below 11?4 on larger diameters, the length is generally one-third to two-thirds the pitch diameter. Curve A also applies for a single key used as a fixed coupling, the length of the key being one to one and one-quarter times the shaft diameter. The stress in the shaft, neglecting stress concentration at the keyway, is about 7500 pounds per square inch. See also Effect of Keyways on Shaft Strength starting on page 283. Curve B represents high-capacity single keys used as fixed couplings for stresses of 9500 pounds per square inch, neglecting stress concentration. Key-length is one to one and onequarter times shaft diameter and both shaft and key are of moderately hard heat-treatedINVOLUTE SPLINES2141steel. This type of connection is commonly used to key commercial flexible couplings to motor or generator shafts. Curve C is for multiple-key fixed splines with lengths of three-quarters to one and onequarter times pitch diameter and shaft hardness of 200–300 BHN. Curve D is for high-capacity splines with lengths one-half to one times the pitch diameter. Hardnesses up to Rockwell C 58 are common and in aircraft applications the shaft is generally hollow to reduce weight. Curve E represents a solid shaft with 65,000 pounds per square inch shear stress. For hollow shafts with inside diameter equal to three-quarters of the outside diameter the shear stress would be 95,000 pounds per square inch. Length of Splines: Fixed splines with lengths of one-third the pitch diameter will have the same shear strength as the shaft, assuming uniform
however, errors in spacing of teeth result in only half the teeth being fully loaded. Therefore, for balanced strength of teeth and shaft the length should be two-thirds the pitch diameter. If weight is not important, however, this may be increased to equal the pitch diameter. In the case of flexible splines, long lengths do not contribute to load carrying capacity when there is misalignment to be accommodated. Maximum effective length for flexible splines may be approximated from Fig. 2. Formulas for Torque Capacity of Involute Splines.—The formulas for torque capacity of 30-degree involute splines given in the following paragraphs are derived largely from an article “When Splines Need Stress Control” by D. W. Dudley, Product Engineering, Dec. 23, 1957. In the formulas that follow the symbols used are as defined on page 2130 with the following additions: Dh = inside diameter of hollow shaft, Ka = application factor from Table 1; Km = load distribution factor from Table 2; Kf = fatigue life factor from Table 3; Kw = wear life factor from Table 4; Le = maximum effective length from Fig. 2, to be used in stress formulas even though the actual l T = transmitted torque, pound-inches. For fixed splines without helix modification, the effective length Le should never exceed
÷ T. Table 1. Spline Application Factors, KaType of Load Uniform (GeneratorFan) 1.0 1.2 Light Shock (Oscillating Pumps, etc.) 1.2 1.3 Intermittent Shock (Actuating Pumps, etc.) 1.5 1.8 Heavy Shock (Punches, Shears, etc.) 1.8 2.1Power Source Uniform (Turbine, Motor) Light Shock (Hydraulic Motor) Medium Shock (Internal Combustion, Engine)Application Factor, Ka2.02.22.42.82142INVOLUTE SPLINESTable 2. Load Distribution Factors, Km, for Misalignment of Flexible SplinesLoad Distribution Factor, Kma Misalignment, inches per inch 0.001 0.002 0.004 0.008a For fixed splines, K =1. m 1? -in. 2Face Width1-in. Face Width 1 1 1 1?2 22-in. Face Width 1 1 1?2 2 2 1?24-in. Face Width 1 1?2 2 2 1?2 31 1 1 1 1?2For fixed splines, Km = 1.Table 3. Fatigue-Life Factors, Kf, for SplinesNo. of Torque Cyclesa 1,000 10,000 100,000 1,000,000 10,000,000 Fatigue-Life Factor, Kf Unidirectional 1.8 1.0 0.5 0.4 0.3 Fully-reversed 1.8 1.0 0.4 0.3 0.2a A torque cycle consists of one start and one stop, not the number of revolutions.Table 4. Wear Life Factors, Kw, for Flexible SplinesNumber of Revolutions of Spline 10,000 100,000 1,000,000 10,000,000 Life Factor, Kw 4.0 2.8 2.0 1.4 Number of Revolutions of Spline 100,000,000 1,000,000,000 10,000,000,000 … Life Factor, Kw 1.0 0.7 0.5 …Wear life factors, unlike fatigue life factors given in Table 3, are based on the total number of revolutions of the spline, since each revolution of a flexible spline results in a complete cycle of rocking motion which contributes to spline wear.Definitions: A fixed spline is one which is either shrink fitted or loosely fitted but piloted with rings at each end to prevent rocking of the spline which results in small axial movements that cause wear. A flexible spline permits some rocking motion such as occurs when the shafts are not perfectly aligned. This flexing or rocking motion causes axial movement and consequently wear of the teeth. Straight-toothed flexible splines can accommodate only small angular misalignments (less than 1 deg.) before wear becomes a serious problem. For greater amounts of misalignment (up to about 5 deg.), crowned splines are preferable to reduce wear and end-loading of the teeth.INVOLUTE SPLINESPitch Diameter of Splines or OD of Keyed Shaft, inches 30 25 20 15 10 7.0 5.0 3.0 2.0 1.5 1.0 0.7 0.5 0.3 100 A Aircraft flexible or single-key commercial B Single-key, high-capacity C High-capacity fixed2143D Aircraft fixed E Limit of spline design (65,000-psi solid shaft)1,00010,000 100,000 Torque, lb-inches1,000,000Fig. 1. Chart for Estimating Involute Spline Size Based on Diameter-Torque Relationships10entmisali gnmen t For f lexib le spl inesmisalignm9 8 Pitch Diameter inches 7 6 5 4 3 2 1 0For maxim umoderate3 4 5 6 7 1 2 Maximum Effective Length Le, inchesFo rfixe ds pli neFor mswithhelix modifi cati on8Fig. 2. Maximum Effective Length for Fixed and Flexible Splines2144INVOLUTE SPLINESShear Stress Under Roots of External Teeth: For a transmitted torque T, the torsional shear stress induced in the shaft under the root diameter of an external spline is: 16TK a S s = -----------------πD re3K f 16TD re K a S s = -----------------------------------4 π ( D re4 – D h )K f for a solid shaft (1)for a hollow shaft(2)The computed stress should not exceed the values in Table 5. Table 5. Allowable Shear Stresses for SplinesHardness Material Steel Steel Steel Surface-hardened Steel Case-hardened Steel Through-hardened Steel (Aircraft Quality) Brinell 160–200 230–260 302–351 — — — Rockwell C — — 33–38 48–53 58–63 42–46 Max. Allowable Shear Stress, psi 20,000 30,000 40,000 40,000 50,000 45,000Shear Stress at the Pitch Diameter of Teeth: The shear stress at the pitch line of the teeth for a transmitted torque T is: 4TK a K m S s = ---------------------DNLe tKf (3)The factor of 4 in (3) assumes that only half the teeth will carry the load because of spacing errors. For poor manufacturing accuracies, change the factor to 6. The computed stress should not exceed the values in Table 5. Compressive Stresses on Sides of Spline Teeth: Allowable compressive stresses on splines are very much lower than for gear teeth since non-uniform load distribution and misalignment result in unequal load sharing and end loading of the teeth. 2TK m K a For flexible splines, S c = ------------------------DNLe hK w 2TK m K a For fixed splines, S c = --------------------------9DNL e hK f (4)(5)In these formulas, h is the depth of engagement of the teeth, which for flat root splines is 0.9/P and for fillet root splines is 1/P, approximately. The stresses computed from Formulas (4) and (5) should not exceed the values in Table 6.INVOLUTE SPLINESTable 6. Allowable Compressive Stresses for SplinesHardness Rockwell C — — 33–38 48–53 58–632145Material Steel Steel Steel Surface-hardened Steel Case-hardened SteelBrinell 160–200 230–260 302–351 — —Max. Allowable Compressive Stress, psi Straight Crowned 1,500 6,000 2,000 3,000 4,000 5,000 8,000 12,000 16,000 20,000Bursting Stresses on Splines: Internal splines may burst due to three kinds of tensile stress: 1) tensile stress due to the radial component of
2) centri and 3) tensile stress due to the tangential force at the pitch line causing bending of the teeth. T tan φ (6) Radial load tensile stress, S 1 = ---------------πDt w L where tw = wall thickness of internal spline = outside diameter of spline sleeve minus spline major diameter, all divided by 2. L = full length of spline. 1.656 × ( rpm ) 2 ( D oi2 + 0.212D ri2) Centrifugal tensile stress, S 2 = ------------------------------------------------------------------------------1, 000, 000 where Doi = outside diameter of spline sleeve. 4T Beam loading tensile stress, S 3 = ---------------D 2 Le Y (8) (7)In this equation, Y is the Lewis form factor obtained from a tooth layout. For internal splines of 30-deg. pressure angle a value of Y = 1.5 is a satisfactory estimate. The factor 4 in (8) assumes that only half the teeth are carrying the load. The total tensile stress tending to burst the rim of the external member is: St = [KaKm (S1 + S3) + S2]/Kf; and should be less than those in Table 7. Table 7. Allowable Tensile Stresses for SplinesHardness Material Steel Steel Steel Surface-hardened Steel Case-hardened Steel Through-hardened Steel Brinell 160–200 230–260 302–351 — — — Rockwell C — — 33–38 48–53 58?63 42–46 Max. Allowable Stress, psi 22,000 32,000 45,000 45,000 55,000 50,000Crowned Splines for Large Misalignments.—As mentioned on page 2142, crowned splines can accommodate misalignments of up to about 5 degrees. Crowned splineshave2146INVOLUTE SPLINESconsiderably less capacity than straight splines of the same size if both are operating with precise alignment. However, when large misalignments exist, the crowned spline has greater capacity. American Standard tooth forms may be used for crowned external members so that they may be mated with straight internal members of Standard form.The accompanying diagram of a crowned spline shows the radius of the crown r1; the radius of curvature of the crowned tooth, r2; the pitch diameter of the spline, D; the face width, F; and the relief or crown height A at the ends of the teeth. The crown height A should always be made somewhat greater than one-half the face width multiplied by the tangent of the misalignment angle. For a crown height A, the approximate radius of curvature r2 is F2 ÷ 8A, and r1 = r2 tan φ, where φ is the pressure angle of the spline. For a torque T, the compressive stress on the teeth is: S c = 2290 2T ÷ DNhr 2 ; and should be less than the value in Table 6. Fretting Damage to Splines and Other Machine Elements.—Fretting is wear that occurs when cyclic loading, such as vibration, causes two surfaces in intimate contact to undergo small oscillatory motions with respect to each other. During fretting, high points or asperities of the mating surfaces adhere to each other and small particles are pulled out, leaving minute, shallow pits and a powdery debris. In steel parts exposed to air, the metallic debris oxidizes rapidly and forms a red, rustl hence, the coined designation “fretting corrosion.” Fretting is mechanical in origin and has been observed in most materials, including those that do not oxidize, such as gold, platinum, hence, the corrosion accompanying fretting of steel parts is a secondary factor. Fretting can occur in the operation of machinery subject to motion or vibration or both. It ca the debris m and fatigue failure may be accelerated because stress levels to initiate fatigue in fretted parts are much lower than for undamaged material. Sites for fretting damage inclu splined, bolted, keyed, pinned, betwee flexi between le small amplitude-of- and electrical contacts. Vibration or cyclic loadings are the main causes of fretting. If these factors cannot be eliminated, greater clamping force may reduce movement but, if not effective, may actually worsen the damage. Lubrication may delay hard plating or surface hardening methods may be effective, not by reducing fretting, but by increasing the fatigue strength of the material. Plating soft materials having inherent lubricity onto contacting surfaces is effective until the plating wears through. Involute Spline Inspection Methods.—Spline gages are used for routine inspection of production parts.INVOLUTE SPLINES2147Analytical inspection, which is the measurement of individual dimensions and variations, may be required: A) To supplement inspection by gages, for example, where NOT GO composite gages are used in place of NOT GO sector gages and variations must be controlled. B) To evaluate parts rejected by gages. C) For prototype parts or short runs where spline gages are not used. D) To supplement inspection by gages where each individual variation must be restrained from assuming too great a portion of the tolerance between the minimum material actual and the maximum material effective dimensions. Inspection with Gages.—A variety of gages is used in the inspection of involute splines. Types of Gages: A composite spline gage has a full complement of teeth. A sector spline gage has two diametrically opposite groups of teeth. A sector plug gage with only two teeth per sector is also known as a “paddle gage.” A sector ring gage with only two teeth per sector is also known as a “snap ring gage.” A progressive gage is a gage consisting of two or more adjacent sections with different inspection functions. Progressive GO gages are physical combinations of GO gage members that check consecutively first one feature or one group of features, then their relationship to other features. GO and NOT GO gages may also be combined physically to form a progressive gage.Fig. 3. Space width and tooth-thickness inspection.GO and NOT GO Gages: GO gages are used to inspect maximum material conditions (maximum external, minimum internal dimensions). They may be used to inspect an individual dimension or the relationship between two or more functional dimensions. They control the minimum looseness or maximum interference. NOT GO gages are used to inspect minimum material conditions (minimum external, maximum internal dimensions), thereby controlling the maximum looseness or minimum interference. Unless otherwise agreed upon, a product is acceptable only if the NOT GO gage does not enter or go on the part. A NOT GO gage can be used to inspect only one dimension. An attempt at simultaneous NOT GO inspection of more than one dimension could result in failure of such a gage to enter or go on (acceptance of part), even though all but one of the dimensions were outside product limits. In the event all dimensions are outside the limits, their relationship could be such as to allow acceptance. Effective and Actual Dimensions: The effective space width and tooth thickness are inspected by means of an accurate mating member in the form of a composite spline gage. The actual space width and tooth thickness are inspected with sector plug and ring gages, or by measurements with pins. Measurements with Pins.—The actual space width of internal splines, and the actual tooth thickness of external splines, may be measured with pins. These measurements do not determine the fit between mating parts, but may be used as part of the analytic inspection of splines to evaluate the effective space width or effective tooth thickness by approximation.2148METRIC MODULE INVOLUTE SPLINESFormulas for 2-Pin Measurement: For measurement between pins of internal splines using the symbols given on page 2130: 1) Find involute of pressure angle at pin center: inv φ i = s ? D + inv φ d – d i ? D b 2) Find the value of φi, in degrees, in the involute function tables beginning on page 98. Find sec φi = 1/cosine φi in the trig tables, pages 94 through 96, using interpolation to obtain higher accuracy. 3) Compute measurement, Mi, between pins: For even numbers of teeth: Mi = Db sec φi ? di For odd numbers of teeth: Mi = (Db cos 90°/N) sec φi ? di where: di =1.7280/P for 30° and 37.5° standard pressure angle (φD) splines di =1.9200/P for 45° pressure angle splines For measurement over pins of external splines: 1) Find involute of pressure angle at pin center: inv φ e = t ? D + inv φ D + d e ? D b – π ? N 2) Find the value of φe and sec φe from the involute function tables beginning on page 98. 3) Compute measurement, Me, over pins: For even numbers of teeth: Me = Db sec φe + de For odd numbers of teeth: Mi = (Db cos 90°/N) sec φe ? de where de =1.9200/P for all external splines Example:Find the measurement between pins for maximum actual space width of an internal spline of 30° pressure angle, tolerance class 4, 3?6 diametral pitch, and 20 teeth. The maximum actual space width to be substituted for s in Step 1 above is obtained as follows: In Table 5, page 2137, the maximum actual space width is the sum of the minimum effective space width (second column) and λ + m (third column). The minimum effective space width sv from Table 2, page 2131, is π/2P = π/(2 × 3). The values of λ and m from Table 4, page 2134, are, for a class 4 fit, 3?6 diametral pitch, 20-tooth spline: λ = 0.0027 × 0.71 = 0.00192; and m = 0.00176 × 0.71 = 0.00125, so that s = 0.52360 + 0.00192 + 0.00125 = 0.52677. Other values required for Step 1 are: D =N/P = 20?3 = 6.66666 invφD = inv 30° = 0.053751 from a calculator di =1.7280?3 = 0.57600 Db =D cos φD = 6.66666 × 0.86603 = 5.77353 The computation is made as follows: 1) inv φi = 0.66 + 0.053751 ? 0.53 = 0.03300 2) From a calculator, φi = 25°46.18′ and sec φi = 1.11044 3) Mi = 5.77353 × 1.11044 ? 0.57600 = 5.8352 inches 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, inchbased, 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*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 too 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.METRIC MODULE INVOLUTE SPLINES2149which 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. Many of the features of the previous standard, ANSI B92.1-1970 (R1993), have been retained such as: 30-, 37.5-, and 45-de flat root and f the four tolerance classes 4, 5, 6, and 7; tables for a and the effective fit concept. Among the major differences are: use of modules of from 0.25 through 10 mm in plac dimensions in millimete the “basic rack”; removal of th and use of ISO symbols in place of those used previously. Also, provision 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 f 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 produce 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 S these differences are shown in Table 1.2150METRIC MODULE INVOLUTE SPLINESTable 1. Comparison of Symbols Used in ANSI B92.2M-1980 (R1989) and Those in ANSI B92.1-1970, R1993Symbol Symbol Meaning of Symbol theoretical clearance effective clearance form clearance pitch diameter base diameter pin contact diameter, external spline pin contact diameter, internal spline 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. 1a, 1b, 1c, and 1d 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 B92.2M m … … Pb p π rfe rfi Ebsc Emax Emin EV Sbsc Smax Smin SV α αD αci αce αi αe αFe αFi es B92.1 … P Ps … p π rf rf sv min s s sv tv max t t tv φ φD φci φce φi φe φF φF … module diametral pitch stub pitch = 2P base pitch circular pitch 3. 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. 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.modification for required fit class=cv min (Table 3) tooth thick, size modifiers (called fundamental deviation in ISO R286), Table 3 space width size modifier (called fundamental deviation in ISO R286), Table 3 Meaning of SymbolB92.2M c cv cF D DB dce dci DEE DEI DFE DFI DIE DII DRE DRI hs λ INV α KE KI g gw gγ T MREB92.1 … cv cF D Db Dce Dci Do Dri DFe DFi Dre Di de di … λ … Ke Ki L … … m MeMRIMimeas. bet. 2 pins, int. splineh, f, e, or d H… …ZNnumber of teethDimensions and Tolerances: Dimensions and tolerances of splines made to the 1980 Standard may be calculated using the formulas given in Table 2. 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 for these, the range of from 0.25 to 2.5 module applies.Table 2. Formulas for Dimensions and Tolerances for All Fit Classes—Metric Module Involute SplinesFormula 30-Degree Flat Root Term 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, Ext Min Major Diam. Ext Ebsc EV min E max E min EV max DEE max DEE min m(Z + 1) ? es/tan αDb 0.5πm 0.5πm EV min + (T + λ) for classes 4, 5, 6, and 7 (see Table 4 for T + λ) EV min + λ (see text on page 2153 for λ) E max ? λ (see text on page 2153 for λ) m(Z + 1) ? es/tan αDb m(Z + 0.9) ? es/tan αDb m(Z + 0.8) ? es/tan αDb DEE max ? (0.2m0.667 ? 0.01m?0.5)a Symbol D DB p pb es DEI min DEI max DFI DII min DII max m(Z + 1) + 2cF m(Z + 1.5) 0.5 to 10 module mZ mZ cos αD πm πm cos αD According to selected fit class, H/h, H/f, H/e, or H/d (see Table 3) m(Z + 1.8) DEI min + (T + λ)/tan αD (see Note 1) m(Z + 1) + 2cF DFE + 2cF (see Note 2) DII min + (0.2m0.667 ? 0.01m?0.5)a m(Z + 0.9) + 2cF m(Z + 0.8) + 2cF m(Z + 1.4) m(Z + 1.2) 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 moduleMETRIC MODULE INVOLUTE SPLINESForm Diam, ExternalDFE2×( 0.5DB ) 20.5es h s + ? -------------- ? ? tan α D? + 0.5D sin α D – ------------------------------sin α Dm(Z ? 1.4) ? es/tan αDb2Max Minor Diam, ExtDIE maxm(Z ? 1.5) ? es/tan αDbm(Z ? 1.8) ? es/tan αDbm(Z ? 1.2) ? es/tan αDb2151Table 2. Formulas for Dimensions and Tolerances for All Fit Classes—Metric Module Involute SplinesFormula 30-Degree Flat Root Term 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 Sbsc SV max S min S max SV min (T + λ) 0.5πm Sbsc ? es SV max ? (T + λ) for classes 4, 5, 6, and 7 (see Table 4 for T + λ) SV max ? λ (see text on page 2153 for λ) S min + λ (see text on page 2153 for λ) See formulas in Table 4 Symbol DIE min 0.5 to 10 module 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 module2152DIE max ? (T + λ)/tan αD (see Note 1)METRIC MODULE INVOLUTE SPLINESMachining Tolerance on Circular Space Width or Tooth ThicknessTT = (T + λ) from Table 4 ? λ from text on page 2153.Effective Variation Allowed on Circular Space Width or Tooth Thickness Form Clearance Rack Dimensionλ cF hsSee text on page m 0.6m(see Fig. 1a) 0.6m(see Fig. 1b) 0.55m(see Fig. 1c) 0.5m(see Fig. 1d)a Values of (0.2m0.667 ? 0.01m?0.5) are as follows: for 10 module, 0.93; for 8 module, 0.80; for 6 module, 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 module, 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; for 0.75 module, 0.15; for 0.5 module, 0.11; and for 0.25 module, 0.06. b See Table 6 for values of es/tan α . D Note 1: Use (T + λ) for class 7 from Table 4. Note 2: For all types of fit, always use the DFE value corresponding to the H/h fit.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 3 are fundamental deviations selected from ISO R286, “ISO System of Limits and Fits.” They are applied to theMETRIC MODULE INVOLUTE SPLINES2153external 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 minimum effective clearance cv. Table 3. Tooth Thickness Modification, es, for Selected Spline Fit ClassesExternal Splinesa Selected Fit Class d e f h Tooth Thickness Modification (Reduction) Relative to Basic Tooth Thickness at Pitch Diameter, es, in mm 0.020 0.030 0.040 0.050 0.065 0.080 0.100 0.120 0.014 0.020 0.025 0.032 0.040 0.050 0.060 0.072 0.006 0.010 0.013 0.016 0.020 0.025 0.030 0.036 0 0 0 0 0 0 0 0 External Splinesa Selected Fit Class d e f h Tooth Thickness Modification (Reduction) Relative to Basic Tooth Thickness at Pitch Diameter, es, in mm 0.145 0.170 0.190 0.210 0.230 0.260 0.290 0.320 0.085 0.100 0.110 0.125 0.135 0.145 0.160 0.170 0.043 0.050 0.056 0.062 0.068 0.076 0.080 0.086 0 0 0 0 0 0 0 0Pitch Diameter in mm, D ≤3 & 3 to 6 & 6 to 10 & 10 to 18 & 18 to 30 & 30 to 50 & 50 to 80 & 80 to 120Pitch Diameter in mm, D & 120 to 180 & 180 to 250 & 250 to 315 & 315 to 400 & 400 to 500 & 500 to 630 & 630 to 800 & 800 to 1000a Internal splines are fit class H and have space width modification from basic space 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 see Fig. 1a, 1b, 1c, and 1d. 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 4, is the sum of Effective Variation, λ, and a Machining Tolerance, T. Table 4. Space Width and Tooth Thickness Total Tolerance, (T + λ), in MillimetersSpline Tolerance Class 4 5 Formula for Total Tolerance, (T + λ) 10i* + 40i** 16i* + 64i** Spline Formula for TolerTotal Toler- In these formulas, i* and i** are tolerance units ance ance, based upon pitch diameter and tooth thickness, Class (T + λ) respectively: 6 25i* + 100i** ? i = 0.001 ( 0.45 3 D + 0.001D )for D ≤ 500 mm 7 40i* + 160i**= 0.001 ( 0.004D + 2.1 ) for D & 500mm i** = 0.001 ( 0.45 3 S bsc + 0.001S bsc )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: λ = 0.6 ( F p ) 2 + ( f f ) 2 + ( F β ) 2 millimeters The above variation is based upon a length of engagement equal to one-half the pitch di 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 5.2154METRIC MODULE INVOLUTE SPLINESTable 5. Formulas for Fp, ff , and Fβ used to calculate λSpline Tolerance Class 4 5 6 7Total Index Variation, in mm, Fp0.001 ( 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 )Total Profile Variation, in mm, ff 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]Total Lead Variation, in mm, Fβ0.001 ( 0.8 g + 4 ) 0.001 ( 1.0 g + 5 ) 0.001 ( 1.25 g + 6.3 ) 0.001 ( 2 g + 10 )g = length of spline in millimeters.Table 6. Reduction, es/tan αD, of External Spline Major and Minor Diameters Required for Selected Fit ClassesStandard Pressure Angle, in Degrees 30 Pitch Diameter D in mm ≤3 &3 to 6 & 6 to 10 & 10 to 18 & 18 to 30 & 30 to 50 & 50 to 80 & 80 to 120 & 120 to 180 & 180 to 250 & 250 to 315 & 315 to 400 & 400 to 500 & 500 to 630 & 630 to 800 & 800 to
0.052 0.069 0.087 0.113 0.139 0.173 0.208 0.251 0.294 0.329 0.364 0.398 0.450 0.502 0.554 37.5 45 30 37.5 45 30 37.5 45 AllClasses of Fit d e es/tan αD in millimeters 0.026 0.039 0.052 0.065 0.085 0.104 0.130 0.156 0.189 0.222 0.248 0.274 0.300 0.339 0.378 0.417 0.020 0.030 0.040 0.050 0.065 0.080 0.100 0.120 0.145 0.170 0.190 0.210 0.230 0.260 0.290 0.320 0.024 0.035 0.043 0.055 0.069 0.087 0.104 0.125 0.147 0.173 0.191 0.217 0.234 0.251 0.277 0.294 0.018 0.026 0.033 0.042 0.052 0.065 0.078 0.094 0.111 0.130 0.143 0.163 0.176 0.189 0.209 0.222 0.014 0.020 0.025 0.032 0.040 0.050 0.060 0.072 0.085 0.100 0.110 0.125 0.135 0.145 0.160 0.170 0.010 0.017 0.023 0.028 0.035 0.043 0.052 0.062 0.074 0.087 0.097 0.107 0.118 0.132 0.139 0.149 0.008 0.013 0.017 0.021 0.026 0.033 0.039 0.047 0.056 0.065 0.073 0.081 0.089 0.099 0.104 0.112 0.006 0.010 0.013 0.016 0.020 0.025 0.030 0.036 0.043 0.050 0.056 0.062 0.068 0.076 0.080 0.086 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f hThese values are used with the applicable formulas in Table 2.Machining Tolerance: A value for machining tolerance may be obtained by subtracting the effective variation, λ, from the total tolerance (T + λ). Design requirements or specific processes used in spline manufacture may require a different amount of machining tolerance in relation to the total tolerance.METRIC MODULE INVOLUTE SPLINES2155Fig. 1a. Profile of Basic Rack for 30° Flat Root SplineFig. 1b. Profile of Basic Rack for 30° Fillet Root SplineFig. 1c. Profile of Basic Rack for 37.5° Fillet Root SplineFig. 1d. Profile of Basic Rack for 45° Fillet Root Spline
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