ANSI B921-1970(R1993) SAE美国渐开线花键标准-Word完整版 (请关注中文翻译版)

ANSI B921-1970(R1993) SAE美国渐开线花键标准-Word完整版 (请关注中文翻译版) Machinery's Handbook 28th Edition INVOLUTE SPLINES 2157 SPLINES AND SERRATIONS A splined shaft is one having a series of parallel keys formed integrally with the shaft and mating with corresponding grooves cut in a hub or fitting; this arrangement is in contrast to a shaft having a series of keys or feathers fitted into slots cut into the shaft. The latter construction weakens the shaft to a considerable degree because of the slots cut into it and consequently, reduces its torque-transmitting capacity. Splined shafts are most generally used in three types of applications: 1 ) for coupling shafts when relatively heavy torques are to be transmitted without slippage; 2) for trans- mitting power to slidably-mounted or permanently-fixed gears, pulleys, and other rotating members; and 3) for attaching parts that may require removal for indexing or change in angular position. Splines having straight-sided teeth have been used in many applications (see SAE Paral- lel Side Splines for Soft Broached Holes in Fittings); however, the use of splines with teeth of involute profile has steadily increased since 1) involute spline couplings have greater torque-transmitting capacity than any other type; 2) they can be produced by the same techniques and equipment as is used to cut gears; and 3) they have a self-centering action under load even when there is backlash between mating members. Involute Splines American National Standard Involute Splines*.— These splines or multiple keys are similar in form to internal and external involute gears. The general practice is to form the external splines either by hobbing, rolling, or on a gear shaper, and internal splines either by broaching or on a gear shaper. The internal spline is held to basic dimensions and the external spline is varied to control the fit. Involute splines have maximum strength at the base, can be accurately spaced and are self-centering, thus equalizing the bearing and stresses, and they can be measured and fitted accurately. In American National Standard ANSI B92.1-1970 (R 1993), many features of the 1960 standard are retained; plus the addition of three tolerance classes, for a total of four. The term ―involute serration,‖ formerly applied to involute splines with 45-degree pressure angle, has been deleted and the standard now includes involute splines with 30-, 37.5-, and 45-degree pressure angles. Tables for these splines have been rearranged accordingly. The term ―serration‖ will no longer apply to splines covered by this Standard. The Standard has only one fit class for all side fit splines; the former Class 2 fit. Class 1 fit has been deleted because of its infrequent use. The major diameter of the flat root side fit spline has been changed and a tolerance applied to include the range of the 1950 and the 1960 standards. The interchangeability limitations with splines made to previous standards are given later in the section entitled ―Interchangeability.‖ There have been no tolerance nor fit changes to the major diameter fit section. The Standard recognizes the fact 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, on side fit splines, the internal spline major diameter now 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 do not need any additional control. The spline specification tables now include a greater number of tolerance level selections. These tolerance classes were added for greater selection to suit end product needs. The selections differ only in the tolerance as applied to space width and tooth thickness. * See American National Standard ANSI B92.2M-1980 (R1989), Metric Module Involute Splines; also see page 2177. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2158 The tolerance class used in ASA B5.15-1960 is the basis and is now designated as tolerance Class 5. The new tolerance classes are based on the following formulas: Tolerance Class 4 = Tolerance Class 5 × 0.71 Tolerance Class 6 = Tolerance Class 5 × 1.40 Tolerance Class 7 = Tolerance Class 5 × 2.00 All dimensions listed in this standard are for the finished part. Therefore, any compensation that must be made for operations that take place during processing, such as heat treatment, must be taken into account when selecting the tolerance level for manufacturing. The standard has the same internal minimum effective space width and external maxi- mum effective tooth thickness for all tolerance classes and has two types of fit. For tooth side fits, the minimum effective space width and the maximum effective tooth thickness are of equal value. This basic concept makes it possible to have interchangeable assembly between mating splines where they are made to this standard regardless of the tolerance class of the individual members. A tolerance class ―mix‖ of mating members is thus allowed, which often is an advantage where 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 instance, assigning a Class 5 tolerance to one member and Class 7 to its mate will provide an assembly tolerance in the Class 6 range. The maximum effective tooth thickness is less than the minimum effective space width for major diameter fits to allow for eccentricity variations. In the event the fit as provided in this standard does not satisfy a particular design need and a specific amount of effective clearance or press fit is desired, the change should be made only to the external spline by a reduction or an increase in effective tooth thickness and a like change in actual tooth thickness. The minimum effective space width, in this standard, is always basic. The basic minimum effective space width should always be retained when special designs are derived from the concept of this standard. Terms Applied to Involute Splines.— The following definitions of involute spline terms, here listed in alphabetical order, are given in the American National Standard. Some of these terms are illustrated in the diagram in Table 6. Active Spline Length (La) is the length of spline that contacts the mating spline. On sliding splines, it exceeds the length of engagement. Actual Space Width (s) is the circular width on the pitch circle of any single space considering an infinitely thin increment of axial spline length. Actual Tooth Thickness (t) is the circular thickness on the pitch circle of any single tooth considering an infinitely thin increment of axial spline length. Alignment Variation is the variation of the effective spline axis with respect to the refer- ence axis (see Fig. 1c). Base Circle is the circle from which involute spline tooth profiles are constructed. Base Diameter (Db) is the diameter of the base circle. Basic Space Width is the basic space width for 30-degree pressure angle splines; half the circular pitch. The basic space width for 37.5- and 45-degree pressure angle splines, how- ever, is greater than half the circular pitch. The teeth are proportioned so that the external tooth, at its base, has about the same thickness as the internal tooth at the form diameter. This proportioning results in greater minor diameters than those of comparable involute splines of 30-degree pressure angle. Circular Pitch (p) is the distance along the pitch circle between corresponding points of adjacent spline teeth. Depth of Engagement is the 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. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2159 Diametral Pitch (P) is the number of spline teeth per inch of pitch diameter. The diametral pitch determines the circular pitch and the basic space width or tooth thickness. In con- junction with the number of teeth, it also determines the pitch diameter. (See also Pitch.) Effective Clearance (cv) is the effective space width of the internal spline minus the effective tooth thickness of the mating external spline. Effective Space Width (Sv) of an internal spline is equal to the circular tooth thickness on the pitch circle of an imaginary perfect external spline that would fit the internal spline without looseness or interference considering engagement of the entire axial length of the spline. The minimum effective space width of the internal spline is always basic, as shown in Table 3. Fit variations may be obtained by adjusting the tooth thickness of the external spline. Three Types of Involute Spline Variations Center Lines of Teeth Reference Axis Fig. 1a. Lead Variation Center Lines of Teeth Reference Axis Fig. 1b. Parallelism Variation Effective Spline Axis Reference Axis Fig. 1c. Alignment Variation Effective Tooth Thickness (tv) of an external spline is equal to the circular space width on the pitch circle of an imaginary perfect internal spline that would fit the external spline without looseness or interference, considering engagement of the entire axial length of the spline. Effective Variation is the accumulated effect of the spline variations on the fit with the mating part. External Spline is a spline formed on the outer surface of a cylinder. Fillet is the concave portion of the tooth profile that joins the sides to the bottom of the space. Fillet Root Splines are those in which a single fillet in the general form of an arc joins the sides of adjacent teeth. Flat Root Splines are those in which fillets join the arcs of major or minor circles to the tooth sides. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2160 Form 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 (c) is the radial depth of involute profile beyond the depth of engagement F 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 (D, D) the diameter of the form circle. FeFi 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 (L) is the axial length of contact between mating splines. q 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 (D, D) is the diameter of the major circle. ori Minor Circle is the circle formed by the innermost surface of the spline. It is the root cir- cle 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 the spline proportions; 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 circle of 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. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2161 Tooth 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 controls the pitch diameter; 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, R1993 cv effective clearance Mi measurement between pins, internal spline cF form clearance D pitch diameter N number of teeth Db base diameter P diametral pitch Dci pin contact diameter, internal spline Ps stub pitch p circular pitch Dce pin contact diameter, external spline rf fillet radius s actual space width, circular DFe form diameter, external spline sv effective space width, circular DFi form diameter, internal spline sc allowable compressive stress, psi Di minor diameter, internal spline ss allowable shear stress, psi Do major diameter, external spline t actual tooth thickness, circular Dre minor diameter, external spline(root) tv effective tooth thickness, circular λ variation allowance Dri major diameter, internal spline(root) ? involute roll angle Φ pressure angle de diameter of measuring pin for spline ΦD standard pressure angle pressure angle at pin contact diameter, internal Φci spline di diameter of measuring pin for spline pressure angle at pin contact diameter, external Φce spline Ke change factor for external spline Ki change factor for internal spline Φi pressure angle at pin center, internal spline L spline length La active spline length Φe pressure angle at pin center, external spline Lg length of engagement m machining tolerance ΦF pressure angle at form diameter Me measurement over pins, external Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2162 Table 2. Formulas for Involute Spline Basic Dimensions ANSI B92.1-1970, R199 30 deg ΦD 37.5 deg ΦD 45 deg ΦD Flat Root Side Fit Flat Root Major Dia Fit Fillet Root Side Fit Fillet Root Side Fit Fillet Root Side Fit Term Symbol 2.5 /5-32 /64 Pitch 3 /6-16 /32 Pitch 2.5/5-48/96 Pitch 2.5/5-48-/96 Pitch 10/20–128/256 Pitch Stub Pitch Ps 2P 2P 2P 2P 2P Pitch Diameter D N/P N/P N/P N/P N/P Base Diameter Db D cos ΦD D cos ΦD D cos ΦD D cos ΦD D cos ΦD Circular Pitch p π/P π/P π/P π/P π/P Minimum Effective sv π/(2 P ) π/(2 P ) π/(2P ) (0.5 π + 0.1 )/P (0.5 π + 0.2 )/P Space Width Major Diameter, D (N+1.35 )/P (N+1)/ P (N+1.8 )/P (N+1.6 )/P (N+1.4 )/P riInternal Major D (N+1)/ P (N+1)/ P (N+1)/ P (N+1)/ P (N+1)/ P oDiameter,External Minor D (N-1)/ P (N-1)/ P (N-1)/ P (N-0.8 )/P (N-0.6 )/P iDiameter,Internal 2.5/5 thru (N-1.35 )/P (N-1.35 )/P (N-1.8 )/P (N-1.3 )/P … 12/24 pitch Minor 16/32 pitch Dia. D (N-1.35 )/P (N-1.35 )/P (N – 2 )/P (N-1.3 )/P … reand finer Ext. 10/20 pitch (N-1.35 )/P (N-1.35 )/P … (N-1.3 )/P (N-1)/ P and finer Form D (N+1)/P + 2cF (N+0.8)/P–0.004+2cF (N+1)/P + 2 cF (N+1)/ P + 2 cF (N+1)/ P + 2 cF FiDiameter,Internal Form D (N-1)/P – 2 cF (N-1)/ P – 2 cF (N-1)/P-2 cF (N-0.8 ) /P – 2cF (N-0.6 )/P–2cF FeDiameter,External Form Clearance cF 0.001 D, with max of 0.010, min of 0.002 (Radial) π = 3.1415927 Note: All spline specification table dimensions in the standard are derived from these basic formulas by application of tolerances. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2163 Table 3. Basic Dimensions for Involute Splines ANSI B92.1-1970, R1993 Pitch, Circular Min Effective Space Width Pitch, Circular Min Effective Space Width P/Ps Pitch, (BASIC), Sv min P/Ps Pitch, (BASIC), Sv min p p 30 deg Φ 37.5degΦ 45 deg Φ 30 deg Φ 37.5 deg Φ 45 deg Φ 2.5 ⁄5 1.2566 0.6283 0.6683 … 20 ⁄40 0.1571 0.0785 0.0835 0.0885 3 ⁄6 1.0472 0.5236 0.5569 … 24 ⁄48 0.1309 0.0654 0.0696 0.0738 4 ⁄8 0.7854 0.3927 0.4177 … 32 ⁄64 0.0982 0.0491 0.0522 0.0553 5 ⁄10 0.6283 0.3142 0.3342 … 40 ⁄80 0.0785 0.0393 0.0418 0.0443 6 ⁄12 0.5236 0.2618 0.2785 … 48 ⁄96 0.0654 0.0327 0.0348 0.0369 8 ⁄16 0.3927 0.1963 0.2088 … 64 ⁄128 0.0491 … … 0.0277 10 ⁄20 0.3142 0.1571 0.1671 0.1771 80 ⁄160 0.0393 … … 0.0221 12 ⁄24 0.2618 0.1309 0.1392 0.1476 128 ⁄256 0.0246 … … 0.0138 16 ⁄32 0.1963 0.0982 0.1044 0.1107 … … … … … 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 pressure angle splines; 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 the sides of the teeth; 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 con- tact 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 Class5 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. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2164 Table 4. Maximum Tolerances for Space Width and Tooth Thickness of Tolerance Class 5 Splines ANSI B92.1-1970, R1993 (Values shown in ten thousandths; 20 = 0.0020) Pitch, P/Ps No.of 2.5 ⁄5 4 ⁄8 and 6 ⁄12 10⁄20 16⁄32 24⁄48 64 ⁄128 128 Teeth and 3 ⁄6 5 ⁄10 and 8 ⁄16 and 12 and 20 and 48 and 80⁄160 ⁄256 ⁄24 ⁄40 ⁄96 N Machining Tolerance, m 10 15.8 14.5 12.5 12 11.7 11.7 9.6 9.5 20 17.6 16 14 13 12.4 12.4 10.2 10 30 18.4 17.5 15.5 14 13.1 13.1 10.8 10.5 40 21.8 19 17 15 13.8 13.8 11.4 — 50 23 20.5 18.5 16 14.5 14.5 — — 60 24.8 22 20 17 15.2 15.2 — — 70 — — — 18 15.9 15.9 — — 80 — — — 19 16.6 16.6 — — 90 — — — 20 17.3 17.3 — — 100 — — — 21 18 18 — — N Variation Allowance, λ 10 23.5 20.3 17 15.7 14.2 12.2 11 9.8 20 27 22.6 19 17.4 15.4 13.4 12 10.6 30 30.5 24.9 21 19.1 16.6 14.6 13 11.4 40 34 27.2 23 21.6 17.8 15.8 14 — 50 37.5 29.5 25 22.5 19 17 — — 60 41 31.8 27 24.2 20.2 18.2 — — 70 — — — 25.9 21.4 19.4 — — 80 — — — 27.6 22.6 20.6 — — 90 — — — 29.3 23.8 21.8 — — 100 — — — 31 25 23 — — N Total Index Variation 10 20 17 15 15 14 12 11 10 20 24 20 18 17 15 13 12 11 30 28 22 20 19 16 15 14 13 40 32 25 22 20 18 16 15 — 50 36 27 25 22 19 17 — — 60 40 30 27 24 20 18 — — 70 — — — 26 21 20 — — 80 — — — 28 22 21 — — 90 — — — 29 24 23 — — 100 — — — 31 25 24 — — N Profile Variation +7 +6 +5 +4 +3 +2 +2 +2 All ?10 ?8 ?7 ?6 ?5 ?4 ?4 ?4 Lead Variation Lg, in. 0.3 0.5 1 2 3 4 5 6 7 8 9 10 Variation 2 3 4 5 6 7 8 9 10 11 12 13 For other tolerance classes: Class 4 = 0.71 × Tabulated value Class 5 = As tabulated in table Class 6 = 1.40 × Tabulated value Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2165 Class 7 = 2.00 × Tabulated value Fillets 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 can- not 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 pro- vide 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 pro- vided 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. Fig. 2. Internal corner clearance. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2166 Spline Variations.— The maximum allowable variations for involute splines are listed in Table 4. Profile 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, pro- file 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 Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2167 tooth thickness by the amount of the effective variation. The 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, R1993 The 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: These dimensions control the minimum effective clearance, and must always be specified. Minimum Actual Space Width and Maximum Actual Tooth Thickness: These dimensions 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 less than anticipated; 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: These dimensions control machining tolerance and limit the effective variation. The spread between these Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2168 dimensions, reduced by the effective variation of the internal and external spline, is the 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: These 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 con- trol. 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 con- trolled 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 mini- mum 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 Major Dia. Fit Flat Root Side Fit Fillet Root Side Fit 1946 Yes No (A) No (A)a Yes (B) Yes (B) Yes (C) 1950b No (A) Yes (B) Yes (C) 1950c No (A) 1957 SAE Yes Yes (C) No (A) Yes 1960 Yes (C) a For exceptions A, B, C, see the paragraph on Exceptions that follows. b Full dedendum. c Short dedendum. Internal Splines: These will mate with older external splines as follows: Year Major Dia. Fit Flat Root Side Fillet Fit Root Side 1946 No (E) No (D) No (D)a Fit Yes (F) 1950 Yes Yes (C) Yes (G) 1957 SAE Yes Yes Yes (G) 1960 Yes Yes a For exceptions C, D, E, F, G, see the paragraph on Exceptions that follows. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2169 Table6.Spline Terms, Symbols, and Drawing Data, 30-Degree Pressure Angle, Flat Root Side Fit ANSI B92.1-1970, R1993 30-Deg Pressure Angle The 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, material, hardness, thermal expansion, etc. Close tolerances or selective size grouping may be required to limit fit variations. Drawing Data Internal Involute Spline Data External Involute Spline Data Flat Root Side Fit Flat Root Side Fit Number of Teeth xx Number of Teeth xx Pitch xx/xx Pitch xx/xx Pressure Angle 30?30?Pressure Angle Base Diameter x.xxxxxx Ref Base Diameter x.xxxxxx Ref Pitch Diameter x.xxxxxx Ref Pitch Diameter x.xxxxxx Ref Major Diameter x.xxx max Major Diameter x.xxx/x.xxx Form Diameter x.xxx Form Diameter x.xxx Minor Diameter x.xxx/x.xxx Minor Diameter x.xxx min Circular Space Width Circular Tooth Thickness Max Actual x.xxxx Max Effective x.xxxx Min Effective x.xxxx Min Actual x.xxxx The following information may be added as The following information may be added as required: required: Max Measurement Between Min Measurement Over Pins x.xxx Ref Pins x.xxxx Ref Pin Diameter x.xxxx Pin Diameter x.xxxx The above drawing data are required for the spline specifications. The standard system is shown; for alternate systems, see Table 5. Number of x's indicates number of decimal places normally used. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2170 Exceptions: 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. 3 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 2385. 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 inches; 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 302. 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 one- quarter times shaft diameter and both shaft and key are of moderately hard heat-treated steel. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2171 Torque, lb-inches Fig. 3. Chart for Estimating Involute Spline Size Based on Diameter-Torque Relationships 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 one- quarter 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 loading of the teeth; 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. 4. 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 2161 with the following additions: Dh = inside diameter of hollow shaft, inches; Ka = application factor from Table 7; Km = load distribution factor from Table 8; Kf = fatigue life factor from Table 9; Kw Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2172 inches Diameter Pitch Maximum Effective Length L, inches e Fig. 4. Maximum Effective Length for Fixed and Flexible Splines = wear life factor from Table 10; Le = maximum effective length from Fig. 4, to be used in stress formulas even though the actual length may be greater; T = transmitted torque, pound-inches. For fixed splines without helix modification, the effective length Le should never 3.5 exceed 5000 D? T. Table 7. Spline Application Factors, Ka Type of Load Uniform Light Shock Intermittent Shock Heavy Shock Power Source (Generator, (Oscillating (Actuating Pumps, (Punches, Fan) Pumps, etc.) etc.) Shears, etc.) Application Factor, Ka Uniform (Turbine, Motor) 1.0 1.2 1.5 1.8 Light Shock (Hydraulic Motor) 1.2 1.3 1.8 2.1 Medium Shock (Internal Combustion, 2.0 2.2 2.4 2.8 Engine) Table 8. Load Distribution Factors, Km, for Misalignment of Flexible Splines Load Distribution Factor, K am Misalignment, inches per inch 1/2-in. Face Width2 1-in. Face Width 2-in. Face Width 4-in. Face Width 0.001 1 1 1 1 1/2 0.002 1 1 1 1/2 2 0.004 1 1 1/2 2 2 1/2 0.008 1 1/2 2 2 1/2 3 a For fixed splines, K=1. mFor fixed splines, K= 1. m Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2173 Table 9. Fatigue-Life Factors, Kf, for Splines Fatigue-Life Factor, Kf No. of Torque Cyclesa Unidirectional Fully-reversed 1,000 1.8 1.8 10,000 1.0 1.0 100,000 0.5 0.4 1,000,000 0.4 0.3 10,000,000 0.3 0.2 a A torque cycle consists of one start and one stop, not the number of revolutions. Table 10. Wear Life Factors, Kw, for Flexible Splines Number of Life Factor, Number of Life Factor, Revolutions of Spline Kw Revolutions of Spline Kw 10,000 4.0 100,000,000 1.0 100,000 2.8 1,000,000,000 0.7 1,000,000 2.0 10,000,000,000 0.5 10,000,000 1.4 … … Wear life factors, unlike fatigue life factors given in Table 9, 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. Shear 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: 16TKa for a solid shaft (1) sS,3re,DK f 16TDKrea S,s for a hollow shaft (2) 44,,(DD)Kre hf The computed stress should not exceed the values in Table 11. Table 11. Allowable Shear, Compressive, and Tensile Stresses for Splines Max. Allowable Stress Hardness Compressive Stress, psi Shear Stress, psi Tensile Stress, psi Material Brinell Rockwell C Straight Crowned 160–200 — 20,000 1,500 6,000 22,000 230–260 — 30,000 2,000 8,000 32,000 Steel 302–351 33–38 40,000 3,000 12,000 45,000 Surface-hardened Steel — 48–53 40,000 4,000 16,000 45,000 Case-hardened Steel — 58–63 50,000 5,000 20,000 55,000 Through-hardened Steel 50,000 — 42–46 45,000 — — (Aircraft Quality) Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2174 Shear Stress at the Pitch Diameter of Teeth: The shear stress at the pitch line of the teeth for a transmitted torque T is: 4TKK amSs, (3) DNLtKef 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 11. 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. For flexible splines, 2TKKam Sc, (4) DNLhKew 2TKK For fixed splines, amcS, (5) 9DNLhKef 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 11. Bursting Stresses on Splines: Internal splines may burst due to three kinds of tensile stress: 1) tensile stress due to the radial component of the transmitted load; 2) centrifugal tensile stress; and 3) tensile stress due to the tangential force at the pitch line causing bending of the teeth. Ttan,Radial load tensile stress, (6) S1, ,DtLw 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. 2221.6556(rpm)(D0.212D)，，oiriCentrifugal tensile stress, (7) S,2 1,000,000 where Doi = outside diameter of spline sleeve. 4T 3S,Beam loading tensile stress, (8) 2eDLY In Equation (8), 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 11. Crowned Splines for Large Misalignments.— As mentioned on page 2173, crowned splines can accommodate misalignments of up to about 5 degrees. Crowned splineshave considerably 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. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2175 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: S22902TDNhrc,, 2 and should be less than the value in Table 11. 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 metal- lic debris oxidizes rapidly and forms a red, rustlike powder or sludge; 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, and nonmetallics; 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 can destroy close fits; the debris may clog moving parts; 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 include interference fits; splined, bolted, keyed, pinned, and riveted joints; between wires in wire rope; flexible shafts and tubes; between leaves in leaf springs; friction clamps; small amplitude-of-oscillation bearings; 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 the onset of damage; 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. Analytical 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. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2176 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 sec- tor 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. 5. 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 out- side 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. Formulas for 2-Pin Measurement Between Pins: For measurement between pins of internal splines using the symbols given on page 2161: 1) Find involute of pressure angle at pin center: dsiinvnv,,，,,i idDD b Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2177 2) Find the value of Φi in degrees, in the involute function tables beginning on page 110. Find sec Φi = 1/cosine Φi in the trig tables, pages 106 through 108, 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 Example: Find the measurement between pins for maximum actual space width of an internal 6 spline of 30? pressure angle, tolerance class 4, 3⁄ 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 2167, the maximum actual space width is the sum of the mini- mum effective space width (second column) and λ + m (third column). The minimum effective space width sv from Table 2, page 2162, is π/2P = π/(2 × 3). The values of λ and m from Table 4, page 2164, 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 inv ΦD = 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 = 0.52677 ⁄6.66666 + 0.053751 ? 0.57600 ⁄5.77353 = 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 Formulas for 2-Pin Measurement Over Pins: For measurement over pins of external splines: Find involute of pressure angle at pin center: dt,e inv,,，,，,invDeDDN b 2) Find the value of Φe and sec Φe from the involute function tables beginning on page 110. 3) Compute measurement, Me, over pins: For even numbers of teeth: Me = Db sec Φe + de For odd numbers of teeth: Me = (Db cos 90?/N) sec Φe + de where de = 1.9200/P for all external splines 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. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2178 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. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2179 Table 12. Comparison of Symbols Used in ANSI B92.2M-1980 (R1989) and Those in ANSI B92.1-1970, R1993 Symbol Symbol B92.2M B92.1 B92.2M B92.1 c … theoretical clearance m … module cv cv effective clearance … P diametral pitch cF cF form clearance … Ps stub pitch = 2P D D pitch diameter Pb … base pitch DB Db base diameter p p circular pitch pin contact diameter, dce Dce π π 3.141592654 external spline pin contact diameter, dci Dci rfe rf fillet rad.,ext.spline internal spline DEE Do major diam., ext. spline rfi rf fillet rad., int. spline DEI Dri major diam., int. spline Ebsc Svmin basic circular space width DFE DFe form diam., ext. spline Emax s max. actual circular space width DFI DFi form diam., int. spline Emin s min. actual circular space width DIE Dre minor diam., ext. spline Ev Sv effective circular space width DII Di minor diam., int. spline Sbsc tvmax basic circular tooth thickness DRE de pin diam., ext. spline Smax t max. actual circular tooth thick DRI di pin diam., int. spline smin t min. actual circular tooth thick hs … see Figs. 6a, 6b, 6c, and 6d SV tv effective circular tooth thick. λ λ effective variation α Φ pressure angle INV a … involute α=tan α? arc α αD ΦD standard pressure angle press. angle at pin contact KE Ke change factor, ext. spline αci Φci diameter, internal spline press. angle at pin contact KI Ki change factor, int. spline αce Φce diameter, external spline press. angle at pin center, internal g L spline length αi Φi spline press. angle at pin center, external gw … active spline length αe Φe spline press. angle at form diameter, gγ … length of engagement αFe ΦF external spline press. angle at form diameter, T m machining tolerance αFi ΦF internal spline ext. spline cir. tooth thick.modifi- meas. over 2 pins, ext. MRE Me es … cation for required fit spline class=cvmin (Table 14) tooth thick, size modifiers (called MRI Mi meas. bet. 2 pins, int. spline h,f,e,or d … fundamental deviation in ISO R286), Table 14 space width size modifier (called Z N number of teeth H … fundamental deviation in ISO R286), Table 14 Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2180 Table 13. Formulas for Dimensions and Tolerances for All Fit Classes— Metric Module Involute Splines Formula 30-Degree Flat 30-Degree Fillet 37.5-Degree Fillet 45-Degree Fillet Term Symbol Root Root Root Root 0.5 to 10 module 0.5 to 10 module 0.5 to 10 module 0.25 to 2.5 module Pitch Diameter D mZ Base Diameter DB mZ cos α D Circular Pitch p πm Base Pitch pb πm cos αD Tooth Thick Mod es According to selected fit class, H/h, H/f, H/e, or H/d (see Table 14) Min Maj. Diam. Int DEI min m(Z + 1.5) m(Z + 1.8) m(Z + 1.4) m(Z + 1.2) Max Maj Diam. Int. DEI max DEI min + (T + λ)/tan αD (see Footnote a) Form Diam, Int. DFI m(Z + 1) + 2c m(Z + 1)+2c m(Z+0.9)+2c m(Z+0.8)+2c FFFFMin Minor Diam, Int DII min DFE + 2cF (see Footnote b) Max Minor Diam,Int DII max DII min + (0.2m0.667 ? 0.01m?0.5) (see Footnote c) Cir Space Width, Basic Ebsc 0.5πm Min Effective EV min 0.5πm Max Actual E max EV min + (T + λ) for classes 4, 5, 6, and 7 (see Table 15 for T + λ) Min Actual E min EV min + λ (see text on page 2181 for λ) Max Effective EV max E max ?λ (see text on page 2181 for λ) Max Major Diam,Extd DEEmax m(Z+1)-es/tanαD m(Z+1)-es/tanαD m(Z+0.9)-es/tanαD m(Z+0.8)-es/tanαD Min Major Diam.Ext DEEmin DEE max ? (0.2m0.667 ? 0.01m?0.5)c Dhs((0.5e，s)/tan),22Form Diam, External DFE bD,2(0.5D)[0.，，5Dsin],Dsin,Max Minor Diam,Extd DIE max m(Z ?1.5)-es/tanαD m(Z ?1.8)?es/tanαD m(Z ?1.4)?es/tanαD m(Z ?1.2)?es/tanαD Min Minor Diam,Ext DIE min DIE max ? (T + λ)/tan αD (see Footnote a) Cir Tooth Thick, Basic Sbsc 0.5πm Max Effective SV max Sbsc ? es Min Actual S min SV max ? (T + λ) for classes 4, 5, 6, and 7 (see Table 15 for T + λ) Max Actual S max SV max ?λ (see text on page 2181 for λ) Min Effective SV min S min + λ (see text on page 2181 for λ) Total Tolerance on Circular Space Width or (T + λ) See formulas in Table 15 Tooth Thickness Machining Toler- ance on Circular Space Width T T = (T + λ) from Table 15 ?λ from text on page 2181. or Tooth Thickness Effective Variation Allowed on Circu- lar λ See text on page 2181. Space Width or Tooth Thickness Form Clearance cF 0.1m Rack Dimension hs 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. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2181 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 Diameter, es, in mm Diameter, es, in mm > 3 to 6 0.030 0.020 0.010 0 180 0.170 0.100 0.050 0 > 180 to > 6 to 10 0.040 0.025 0.013 0 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 > 18 to 30 0.065 0.040 0.020 0 > 250 to 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 > 50 to 80 0.100 0.060 0.030 0 > 315 to 0.290 0.160 0.080 0 400 > 80 to 120 0.120 0.072 0.036 0 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; 500 thus, an H/h fit class has effective clearance cv = 0. > 500 to Note: The values listed in this table are taken from ISO R286 and have been computed on the basis of the 630 geometrical mean of the size ranges shown. Values in boldface type do not comply with any documented rule > 630 to 800 for rounding but are those used by ISO R286; they are used in this table to comply with established > 800 to international practice. 1000 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 Formula for In these formulas, i* and i** are tolerance units Tolerance Tolerance based upon pitch diameter and tooth thickness, Total Tolerance, Total Tolerance, Class Class respectively: (? is radication) T + λ) (T + λ) i?= 0.001 (0.45 *??D+0.001D) for D?500 mm 4 10i* + 40i** 6 25i* + 100i** i?= 0.001 (0.004D + 2.1 ) for D > 500 mm i??= 0.001 (0.45 *? ?(Sbsc) + 0.001 Sbsc ) 5 16i* + 64i** 7 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: 222,,，，0.6(F)(f)(F)pf, 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. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2182 Table 16. Formulas for F, f, and Fλ used to calculate pf β Spline Total Index Variation, in mm, Total Profile Variation, in mm, Total Lead Variation, in Tolerance Fp ff mm,Fβ Class 4 0.001(2.5*?(mZπ/2)+6.3) 0.001[1.6m(1+0.0125Z)+10] 0.001(0.8*?g+4) 5 0.001(3.55*?(mZπ/2)+9) 0.001[2.5m(1+0.0125Z)+16] 0.001(1.0*?g+5) 6 0.001(5*?(mZπ/2)+12.5) 0.001[4m(1+0.0125Z)+25] 0.001(1.25*?g+6.3) 7 0.001(7.1*?(mZπ/2)+18) 0.001[6.3m(1+0.0125Z)+40] 0.001(2*?g+10) g = length of spline in millimeters. Table 17. Reduction, es/tan αD, of External Spline Major and Minor Diameters Required for Selected Fit Classes Standard Pressure Angle, in Degrees 30 37.5 45 30 37.5 45 30 37.5 45 All Pitch Diameter Classes of Fit D in mm d e f h es/tan αD in millimeters ?3 0.035 0.026 0.02 0.024 0.018 0.014 0.01 0.008 0.006 0 >3 to 6 0.052 0.039 0.03 0.035 0.026 0.02 0.017 0.013 0.01 0 > 6 to 10 0.069 0.052 0.04 0.043 0.033 0.025 0.023 0.017 0.013 0 > 10 to 18 0.087 0.065 0.05 0.055 0.042 0.032 0.028 0.021 0.016 0 > 18 to 30 0.113 0.085 0.065 0.069 0.052 0.04 0.035 0.026 0.02 0 > 30 to 50 0.139 0.104 0.08 0.087 0.065 0.05 0.043 0.033 0.025 0 > 50 to 80 0.173 0.13 0.1 0.104 0.078 0.06 0.052 0.039 0.03 0 > 80 to 120 0.208 0.156 0.12 0.125 0.094 0.072 0.062 0.047 0.036 0 > 120 to 180 0.251 0.189 0.145 0.147 0.111 0.085 0.074 0.056 0.043 0 > 180 to 250 0.294 0.222 0.17 0.173 0.13 0.1 0.087 0.065 0.05 0 > 250 to 315 0.329 0.248 0.19 0.191 0.143 0.11 0.097 0.073 0.056 0 > 315 to 400 0.364 0.274 0.21 0.217 0.163 0.125 0.107 0.081 0.062 0 > 400 to 500 0.398 0.3 0.23 0.234 0.176 0.135 0.118 0.089 0.068 0 > 500 to 630 0.45 0.339 0.26 0.251 0.189 0.145 0.132 0.099 0.076 0 > 630 to 800 0.502 0.378 0.29 0.277 0.209 0.16 0.139 0.104 0.08 0 > 800 to 1000 0.554 0.417 0.32 0.294 0.222 0.17 0.149 0.112 0.086 0 These values are used with the applicable formulas in Table 13. 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. Fig. 6a. Profile of Basic Rack for 30? Flat Root Spline Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Machinery's Handbook 28th Edition INVOLUTE SPLINES 2183 Fig. 6b. Profile of Basic Rack for 30? Fillet Root Spline Fig. 6c. Profile of Basic Rack for 37.5? Fillet Root Spline Fig. 6d. Profile of Basic Rack for 45? Fillet Root Spline British Standard Straight Splines.— British Standard BS 2059:1953, ―Straight-sided Splines and Serrations‖, was introduced because of the widespread development and use of splines and because of the increasing use of involute splines it was necessary to provide a separate standard for straight-sided splines. BS 2059 was prepared on the hole basis, the hole being the constant member, and provide for different fits to be obtained by varying the size of the splined or serrated shaft. Part 1 of the standard deals with 6 splines only, irrespective of the shaft diameter, with two depths termed shallow and deep. The splines are bottom fitting with top clearance. The standard contains three different grades of fit, based on the principle of variations in the diameter of the shaft at the root of the splines, in conjunction with variations in the widths of the splines themselves. Fit 1 represents the condition of closest fit and is designed for minimum backlash. Fit 2 has a positive allowance and is designed for ease of assembly, and Fit 3 has a larger positive allowance for applications that can accept such clearances. Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com