SPLINES AND SERRATIONS

Transcription

1 2126 INVOLUTE SPLINES SPLINES AND SERRATIONS mating A splined with shaft corresponding is one having grooves a series cut of in parallel a hub or keys fitting; formed this arrangement integrally with is in the contrast shaft and a shaft having a series of keys or feathers fitted into slots cut into the shaft. The latter construction weakens reduces the its shaft torque-transmitting to a considerable capacity. degree because of the slots cut into it and con- to sequently, shafts Splined when shafts relatively are most heavy generally torques used are in to three be transmitted types of applications: without slippage; 1) for 2) coupling mitting power to slidably-mounted or permanently-fixed gears, pulleys, and other for rotating trans- members; angular position. and 3) for attaching parts that may require removal for indexing or change in lel Splines Side Splines having for straight-sided Soft Broached teeth Holes have in been Fittings); used in however, many applications the use of splines (see SAE with Paral- of involute profile has steadily increased since 1) involute spline couplings have greater teeth torque-transmitting techniques and equipment capacity as than is used any to other cut gears; type; and 2) they 3) they can have be produced a self-centering by the action same under load even when there is backlash between mating members. Involute Splines American similar in form National to internal Standard and external Involute involute Splines*. These gears. The general splines practice or multiple is to keys form are external splines either by hobbing, rolling, or on a gear shaper, and internal splines either the by external broaching spline or is on varied a gear to shaper. control The the fit. internal Involute spline splines is held have to basic maximum dimensions strength and at the the base, stresses, can and be they accurately can be measured spaced and and are fitted self-centering, accurately. thus equalizing the bearing and standard In American are retained; National plus Standard the addition ANSI of B three tolerance (R 1993), classes, many for features a total of of four. the 1960 term involute The angle, has been deleted formerly applied to involute splines with 45-degree pressure serration, 45-degree pressure angles. and Tables the standard for these now splines includes have involute been rearranged splines with accordingly. 30-, 37.5-, The and term will no longer apply to splines covered by this Standard. The serration has been Standard deleted has because only one of fit its class infrequent for all use. side The fit splines; major the diameter former of Class the flat 2 fit. root Class side 1 fit fit spline 1960 standards. has been changed The interchangeability and a tolerance limitations applied to include with splines the range made of to the previous 1950 and standards are given later in the section entitled the There have been no tolerance nor fit changes Interchangeability. to the major diameter fit section. dent The only Standard on the recognizes spline being the within fact that effective proper specifications assembly between from mating the tip of splines the tooth is depen- form diameter. Therefore, on side fit splines, the internal spline major diameter now to the shown as a maximum dimension and the external spline minor diameter is shown as a minimum diameter dimension. must clear The the minimum specified internal form diameter major diameter and thus and do the not maximum need any additional external minor is trol. contions. The These spline tolerance specification classes tables were now added include for greater a greater selection number to of suit tolerance end product level needs. selec- The selections differ only in the tolerance as applied to space widthand tooth thickness. *See see page2148. American National Standard ANSI B92.2M-1980 (R1989), Metric Module Involute Splines; also

2 INVOLUTE SPLINES 2127 ance The tolerance Class 5. The class new used tolerance in ASA classes B are based is the on basis the following and is now formulas: designated as toler- Tolerance Class 4 Tolerance Class 0.71 Tolerance Class 6 Tolerance Class 1.40 Tolerance Class 7 = Tolerance Class tion All that dimensions must be made listed for in this operations standard that are take for the place finished during part. processing, Therefore, such any as compensament, must be taken into account when selecting the tolerance level for manufacturing. heat treatmum The effective standard tooth has the thickness same internal for all minimum tolerance classes effective and space has two width types and of external fit. For maxi- side fits, the minimum effective space width and the maximum effective tooth thickness tooth are between of equal mating value. splines This basic where concept they are makes made it to possible this standard to have regardless interchangeable of the assembly class of the individual members. A tolerance class of mating members tolerance allowed, which often is an advantage where one member is thus mix produce than its mate, and the tolerance applied is to considerably the two units less is such difficult that to satisfies the design need. For instance, it average Class 7 to its mate will provide an assembly assigning tolerance a Class in the 5 tolerance Class 6 range. to one The member maximum and effective fits to allow tooth for thickness eccentricity is less variations. than the minimum effective space width for major diameter and In a the specific event the amount fit as of provided effective in clearance this standard or press does fit not is satisfy desired, a particular the change design should need made only to the external spline by a reduction or an increase in effective tooth thickness be standard, and a like is change always in basic. actual The tooth basic thickness. minimum The effective minimum space effective width space should width, always in this retained when special designs are derived from the concept of this standard. be Terms terms, here Applied listed to in Involute alphabetical Splines. The order, are given following in the American definitions National of involute Standard. spline of these terms are illustrated in the diagram in Tables 6. Some Active Spline Length (La) is the length of spline that contacts the mating spline. On sliding splines, it exceeds the length of engagement. sidering Actual an Space infinitely Width thin (s) is increment the circular of axial width spline on the length. pitch circle of any single space con- considering Actual Tooth an infinitely Thickness thin (t) is increment the circular of axial thickness spline on length. the pitch circle of any single tooth ence Alignment axis (see Variation Fig. 1c). is the variation of the effective spline axis with respect to the refer- Base Circle is the circle from which involute spline tooth profiles are constructed. Base Diameter (Db) is the diameter of the base circle. circular Basic pitch. Space The Width basic is the space basic width space for width for and 30-degree 45-degree pressure pressure angle angle splines; splines, half however, tooth, is at greater its base, than has half about the the circular same pitch. thickness The as teeth the are internal proportioned tooth at so the that form the diameter. external the splines This proportioning of 30-degree results pressure in angle. greater minor diameters than those of comparable involute adjacent Circular spline Pitch teeth. (p) is the distance along the pitch circle between corresponding points of the Depth major of circle Engagement of the external is the radial spline, distance minus corner from the clearance minor circle and/or of chamfer the internal depth. spline to

3 2128 INVOLUTE SPLINES 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 conjunction with the number of teeth, it also determines the pitch diameter. (See also Pitch.) Effective Clearance (c v ) is the effective space width of the internal spline minus the effective tooth thickness of the mating external spline. Effective Space Width (S v ) 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 Reference Axis Center Lines of Teeth Reference Axis Fig. 1a. Lead Variation Center Lines of Teeth Reference Axis Fig. 1b. Parallelism Variation Effective Spline Axis Fig. 1c. Alignment Variation Effective Tooth Thickness (t v ) 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.

4 INVOLUTE SPLINES 2129 tooth Form profile. Circle This is the circle circle along which with defines the tooth the deepest tip circle points (or of start involute of chamfer form control circle) determines internal the spline limits and of near tooth the profile minor requiring circle on control. the external It is located spline. near the major circle on the of the Form Clearance (cf) is the radial depth of involute profile beyond the depth of engagement with between the mating the minor part. circle It allows (internal), for looseness the major between circle (external), mating splines and their and respective for eccentricities pitch Form circles. Diameter (DFe,DFi) the diameter of the form circle. Internal Involute Spline Spline is is a one spline having formed teeth on with the involute inner surface profiles. of a cylinder. tion Lead parallel Variation to the is reference the variation axis, of also the including direction of parallelism the spline and tooth alignment from its intended variations direc- Fig. 1a). Note: Straight (nonhelical) splines have an infinite lead. (see Length of Engagement (Lq) is the axial length of contact between mating splines. tooth Machining thickness. Tolerance (m) is the permissible variation in actual space width or actual circle Major (tooth Circle tip is circle) the circle of the formed external by spline the outermost or the root surface circle of of the the spline. internal It spline. is the outside Major Diameter (Do,Dri) is the diameter of the major circle. cle Minor of the Circle external is the spline circle or the formed inside by circle the innermost (tooth tip surface circle) of of the the internal spline. It spline. is the root cir- Minor Diameter (Dre,Di) is the diameter of the minor circle. thickness Nominal of Clearance the mating is external the actual spline. space It width does not of an define internal the fit spline between minus mating the actual members, tooth because Out of of Roundness the effect is of the variations. Parallelism Variation is variation the variation of the of spline parallelism from a of true a single circular spline configuration. to any other single spline tooth (see Fig. 1b). tooth with respect Pitch (P/Ps) is a combination number of a one-to-two ratio indicating the spline proportions; stub pitch the upper and denotes, or first as number that fractional is the diametral part of an pitch, inch, the the lower basic or radial second length number of engagement, Pitch both Circle above is the and reference below the circle pitch from circle. is the constructed. which all transverse spline tooth dimensions are Pitch Pitch Diameter Point is the (D) intersection is the diameter of the of spline the pitch tooth circle. Pressure Angle (φ) is the angle between a line tangent profile with to an the involute pitch circle. through the point of tangency. Unless otherwise specified, it is the standard and pressure a radial angle. line Profile Spline is Variation a machine is any element variation consisting from the of specified integral tooth keys profile (spline normal teeth) to or the keyways flank. (spaces) Standard equally (Main) spaced Pressure around Angle a circle (φd) or is portion the pressure thereof. angle at the specified pitch diameter Ṡtub Pitch (P s) is a number used to denote the radial distance from the pitch circle to the major spline. circle The stub of the pitch external for splines spline in and this from standard the pitch is twice circle the to the diametral minor circleof pitch. the internal between Total Index the actual Variation and the is the perfect greatest spacing difference of the tooth in any profiles. two teeth (adjacent or otherwise) Total Variation Tolerance Allowance (m λ) is the machining tolerance plus the variation allowance. + (λ) is the permissible effective variation.

5 2130 INVOLUTE SPLINES 12 24, Tooth Proportions. There 16 32, 20 40, 24 48, 32 64, are , pitches: 48 96, 2.5 5, , 3 6, 4 8,5 10, , 6 12, and , 10 20, 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 the is number used in of the teeth formulas per inch given of pitch and is diameter. designated as P. Diametral pitch, as in gears, means the lute Table spline 1 shows teeth of the various symbols pitches. and Table Basic 2 dimensions the formulas are for given basic in tooth Table dimensions 3. of invo- Table 1. American National ANSI B , Standard R1993 Involute Spline Symbols cv effective clearance Mi measurement between pins, internal cf D form pitch clearance diameter N spline number of teeth Db base diameter P diametral pitch Dci pin contact diameter, internal Ps spline p stub circular pitch pitch Dce pin contact diameter, external rf spline s fillet actual radius 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 tv (root) 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 external φd spline standard pressure angle φci pressure angle at pin contact diameter, di diameter spline of measuring pin for internal internal spline φce pressure angle at pin contact diameter, Ke change factor for external spline external spline Ki change factor for internal spline φi L spline length pressure spline angle at pin center, internal La active spline length φe pressure angle at pin center, external Lg m length machining of engagement tolerance spline φf pressure angle at form diameter Me measurement spline over pins, external

6 INVOLUTE SPLINES 2131 Table 2. Formulas for Basic Dimensions ANSI B , R1993 Formula Term Symbol 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 Pitch Pitch Pitch Pitch Pitch Stub 2P 2P 2P 2P 2P Pitch Ps D Pitch Diameter N--- N P --- N P --- N P --- N P --- P Base D Diameter Db D cos φd D cos φd D cos φd D cos φd cos φd Circular Pitch P-- P-- P-- P-- P-- π p π π π π Minimum Space Width Effective sv P π 2P π 2P π 0.5π P π P Major Internal Diameter, N Dri N P N P N P N P P Major External Diameter, N Do N P N P N P N P P Minor Diameter, N N N 0.8 Internal Di P N 1 P P N 0.6 P P

7 2132 INVOLUTE SPLINES Minor Dia. Ext. Term Symbol thru pitch and finer pitch pitch and finer Dre Table 2. (Continued) Formulas for Basic Dimensions ANSI B , R1993 Formula 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 Pitch Pitch Pitch Pitch Pitch N P N P Form Internal Diameter, N DFi P + 2cF N P cF N P + 2cF N 1 Form External Diameter, N DFe P 2cF N 1 P 2cF N P 2cF Form (Radial) Clearance cf 0.001D, with max of 0.010, min of π = All spline specification table dimensions in the standard are derived from these basic formulas by Note: application of tolerances. N P N P N P 2cF P + 2cF N 1 N P P + 2cF N P 2cF

8 INVOLUTE SPLINES 2133 Table 3. Basic Dimensions for Involute Splines ANSI B , R1993 Pitch, Circular Min Effective P/Ps Pitch, (BASIC), Space Width p Sv min Pitch, Circular Min Effective P/Ps Pitch, (BASIC), Space Width p Sv 30 deg min φ 37.5 deg φ 45 deg φ 30 deg φ 37.5 deg φ 45 deg φ Tooth numbers Numbers. The ranging from 6 American to 60 with National a 30- or 37.5-degree Standard covers pressure involute angle splines and from having 6 to tooth with a 45-degree pressure angle. In selecting the number of teeth for a given spline applicationbers of it is teeth well and to keep that the in mind diameters that there of splines are no with advantages odd tooth to numbers, be gained particularly by using odd internal num- 100 splines, opposite are each troublesome other. to measure with pins since no two tooth spaces are diametrically Types ican National and Classes Standard of Involute for involute Spline splines, Fits. Two the side fit, types and of the fits major are covered diameter by fit. the Dimensional tabulated data in for this flat standard root side for fit, 30-degree flat root major pressure diameter angle fit, splines; and fillet but root for only side fit the splines fillet root are Amer- side fit for and 45-degree pressure angle splines. and Side minor Fit: diameters In the side are fit, clearance the mating dimensions. members contact The tooth only sides on the act as sides drivers of the and teeth; centralize major the mating splines. ing. Major The sides Diameter of the Fit: teeth Mating act as parts drivers. for this The fit minor contact diameters at the major are clearance diameter dimensions. for centraliztact The and major location diameter at the fit major provides diameter a minimum with a minimum effective amount clearance of location that will or allow centralizing for con- effect thickness by the tolerance sides of which the teeth. is the The same major as side diameter fit Class fit 5. has only one space width and tooth to A the fillet flat root root may side fit be or specified major diameter for an external fit standard. spline, An even internal though spline it is with otherwise a fillet designed be used only for the side fit. root can Classes and tooth of thickness. Tolerances. This This has been standard done to includes provide four a range classes of tolerances of tolerances for selection on space to width a design need. The classes are variations of the former single tolerance which is now Class suit 5 the and same are based minimum on the effective formulas space shown width in the and footnote maximum of Table effective 4. All tooth tolerance thickness classes limits have that a mix of classes between mating parts is possible. so

9 2134 INVOLUTE SPLINES Table 4. Maximum Tolerances Class 5 Splines for Space ANSI Width B , and Tooth R1993 Thickness of Tolerance (Values shown in ten thousandths; 20 = ) No. Pitch, P/Ps Teeth of and and and and and thru and N Machining Tolerance, m N Variation Allowance, λ N Total Index Variation N Profile Variation All Lead Variation L g, in Variation For other tolerance classes: Class 4 = 0.71 Tabulated value Class 5 As tabulated in table Class Tabulated value Class 7 = 2.00 Tabulated value

10 INVOLUTE SPLINES 2135 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 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 P min P max Fig. 2. Internal corner clearance. Spline Variations. The maximum allowable variations for involute splines are listed in Table 4.

11 2136 INVOLUTE SPLINES point Profile used Variation: to determine The the reference actual profile, space width from or which tooth variations thickness. occur, This passes is either through the pitch the point or the contact point of the standard measuring pins. the Profile tooth. variation Profile variations is positive may in the occur direction at any point of the on space the profile and negative for establishing in the direction effective of fits and are shown in Table 4. thereof Lead Variations: unless otherwise The lead specified. tolerance for the total spline length applies also to any portion variations Out of Roundness: given in Table This 4 condition and requires may no appear further merely allowance. as a However, result of heat index treatment and profile deflection of thin sections may cause out of roundness, which increases index and profile and tabulated. variations. Additional Tolerances tooth for such and/or conditions space width depend tolerance on many must variables allow for and such are therefore conditions. not eter Eccentricity: of side fit splines Eccentricity should of not major cause and contact minor diameters beyond the in form relation diameters to the effective of the mating diam- splines, establish even specific under tolerances. conditions of maximum effective clearance. This standard does not fit Eccentricity splines should of major be absorbed diameters within in the relation maximum to the material effective limits diameters established of major by the diameter ances on major diameter and effective space width or effective tooth thickness. toler- to If each the alignment other and/or of mating the splines, splines it may is affected be necessary by eccentricity to decrease of locating the effective surfaces and relative tooth thickness of the external splines in order to maintain the desired fit condition. actual standard does not include allowances for eccentric location. This Effect file variations, of Spline or Variations. Spline lead variations. variations can be classified as index variations, pro- tooth Index sides Variations: to another. These Because variations the fit depends cause the on clearance the areas with to vary minimum from one clearance, set of mating variations reduce the effective clearance. index ance. Profile Negative Variations: profile Positive variations profile do not variations affect the affect fit but the reduce fit by the reducing contact effective area. clear- the Lead effective Variations: clearance. These variations will cause clearance variations and therefore reduce ation) Variation is less Allowance: than their total, The because effect of areas individual of more spline than variations minimum on clearance the fit (effective can be altered vari- without itive profile changing variation, the fit. the The total variation index allowance variation and is 60 the percent lead of variation the sum for of twice the length the pos- engagement. The variation allowances in Table 4 are based on a lead variation for an of assumed required for length a greater of engagement length of engagement. equal to one-half the pitch diameter. Adjustment may be Effective the same width and Actual as each Dimensions. Although tooth of a perfect mating each external space of spline, an internal the two spline may may not have because of variations of index and profile in the internal spline. To allow the perfect external amount spline of to interference. fit in any position, The resulting all spaces width of the of these internal tooth spline spaces must is then the actual be widened space by width the fit external of the internal spline. spline. The same The effective reasoning space applied width to is an the external tooth thickness spline that of the has perfect variations mating index and profile when mated with a perfect internal spline leads to the concept of effective of tooth variation. thickness, which exceeds the actual tooth thickness by the amount of the effective

12 INVOLUTE SPLINES 2137 external The effective spline is space the effective width of clearance the internal and spline defines minus the the fit of effective the mating tooth parts. thickness (This of statement clearance is strictly represents true only if looseness high points or of backlash. mating parts Negative come effective into contact.) clearance Positive represents effec- the tive tightness or interference. Space actual tooth Width thickness and Tooth within Thickness the machining Limits. The tolerance variation causes corresponding of actual space variations width and effective dimensions, so that there are four limit dimensions for each component part. of These variations are shown diagrammatically in Table 5. Table 5. Specification ANSI Guide B , for Space Width R1993and Tooth Thickness ness The is minimum the same effective as the minimum space width effective is always space basic. width The except maximum for the effective major diameter tooth thick- The major diameter fit maximum effective tooth thickness is less than the minimum effective major space diameter. width by an The amount permissible that allows variation for eccentricity of the effective between clearance the effective is divided spline between and fit. the the minimum internal effective and external tooth splines thickness. to arrive Limits at the for maximum the actual space effective width space and width actual and tooth the thickness are constructed from suitable variation allowances. and Use tooth of Effective thickness and shown Actual in Dimensions. Each Table 5 has a definite of function. the four dimensions for space width dimensions Minimum Effective control the Space minimum Width effective and Maximum clearance, Effective and must Tooth always Thickness: be specified. These sions Minimum cannot Actual be used Space for acceptance Width and Maximum or rejection Actual of parts. Tooth If the Thickness: actual space These width dimen- than the minimum without causing the effective space width to be undersized, or is if less actual tooth thickness is more than the maximum without causing the effective tooth thickness and not to be defective. oversized, The the specification effective variation of these is less dimensions than anticipated; as processing such parts reference are desirable the sions is optional. They are also used to analyze undersize effective space width or oversize dimen- effective caused by tooth excessive thickness effective conditions variation. to determine whether or not these conditions are sions Maximum control Actual machining Space tolerance Width and and Minimum limit the Actual effective Tooth variation. Thickness: The These spread dimen- these dimensions, reduced by the effective variation of the internal and external spline, between is

13 2138 INVOLUTE SPLINES appreciably the maximum less effective than the clearance. variation Where allowance, the effective these dimensions variation must obtained be adjusted in machining in order is to maintain the desired fit. dimensions Maximum Effective define the Space maximum Width effective and Minimum clearance Effective but Tooth they do Thickness: not limit These variation. They may be used, in addition to the maximum actual space width and the minimum effective actual reduction tooth of effective thickness, variations. to prevent The the notation increase inspection of maximum effective clearance due to maximum effective clearance is an assembly requirement, but may be added where optional trol. It will indicate, without necessarily adding inspection time does and not equipment, need absolute that con- actual space width of the internal spline must be held below the maximum, or the actual the less tooth than thickness the allowable of the external variations. spline Where above effective the minimum, variation if machining needs no control methods or result is controlled and by laboratory minimum actual inspection, tooth these thickness. limits may be substituted for maximum actual space in width with Combinations fillet root external of Involute splines Spline where Types. Flat the larger radius root side is desired fit internal on the splines external may spline be used control of stress concentrations. This combination of fits may also be permitted as a design for option mum root by specifying diameter of for the the fillet minimum root external root diameter spline and of noting the external, this as the optional value of the mini- root. internal A design by specifying option may for also the be maximum permitted major to provide diameter, either the flat value root of internal the maximum or fillet major root diameter of the fillet root internal spline and noting this as optional root. Interchangeability. Splines to older standards. Exceptions are made listed to below. this standard may interchange with splines made External Splines: These external splines will mate with older internal splines as follows: Year Major FitDia. Flat Side Root Fit Fillet Side Root Fit 1946 Yes No (A)a No (A) 1950b Yes (B) Yes (B) Yes (C) 1950c 1957 SAE Yes Yes (B) No No (A) (A) Yes Yes (C) (C) 1960 Yes No (A) Yes (C) bfull afor exceptions dedendum. A, B, C, see the paragraph on Exceptions that follows. cshort dedendum. Internal Splines: These will mate with older external splines as follows: Year Major FitDia. Flat Side Root Fit Fillet Side Root Fit Yes No (D)a (F) No Yes(E) No (D) 1957 SAE Yes (G) Yes Yes(C) 1960 Yes (G) Yes Yes afor exceptions C, D, E, F, G, see the paragraph on Exceptions that follows.

14 INVOLUTE SPLINES 2139 Table 6. Spline Terms, Symbols, and Drawing Data, 30-Degree Pressure Angle, Flat Root Side Fit ANSI B , R1993 Space Width (Circular) s = Actual s v = Effective Internal Spline 30-Deg Pressure Angle Tooth Thickness (Circular) t = Actual t v = Effective Circular Pitch P Fillet Form Clearance C F Pitch Dia. D Ref Optional External Spline Major Dia. D o D ri Major Dia. D i D re C F Major Dia. D Fe D Fi 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, materila, hardness, thermal expansion, etc. Close tolerances or selective size grouping may be required to limit fit variations. Flat Root Side Fit Internal Involute Spline Data Drawing Data Flat Root Side Fit External Involute Spline Data Number of Teeth xx Number of Teeth xx Pitch xx/xx Pitch xx/xx Pressure Angle 30 Pressure Angle 30 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 required: The following information may be added as required: Max Measurement Between Pins x.xxx Ref Min Measurement Over 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.

15 2140 INVOLUTE SPLINES Exceptions: internal A) The form external diameter major on diameter, flat root side unless fit chamfered splines. Internal or reduced, splines may made interfere to the 1957 with and the 1960 standard. standards had the same dimensions as shown for the major diameter fit splines in this interfere B) For 15 with teeth the or form less, diameter the minor of the diameter external of spline. the internal spline, unless chamfered, will interfere C) For 9 with teeth form or less, diameter the minor of the diameter external spline. of the internal spline, unless chamfered, will diameter. 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 may F) For not 10 clear teeth the or internal less, the form minimum diameter. chamfer on the major diameter of the external spline may G) not Depending clear the upon internal the pitch form diameter. of the spline, the minimum chamfer on the major diameter Drawing information Data. It on detail is drawings important of splines. that uniform Much specifications misunderstanding be used will to be show avoided complete lowing the suggested arrangement of dimensions and data as given in Table 6. The number by fol- of spline x's indicates specifications, the number it is usually of decimal not necessary places normally to show a used. graphic With illustration this tabulated of the type spline of teeth. Spline manufacturing Data and purposes. Reference Pitch Dimensions. Spline and pressure angle are data not subject are used to individual for engineering inspection. and ification, As used or in note this standard, when that reference dimension, is an specification, added notation or note or modifier is: to a dimension, spec- 1) 2) Repeated Needed to for define drawing a nonfeature clarification. ated. datum or basis from which a form or feature is genersions 3) Needed are developed. to define a nonfeature dimension from which other specifications or dimen- specified. 4) Needed to define a nonfeature dimension at which toleranced sizes of a feature are developed 5) Needed or to added define as a useful nonfeature information. dimension from which control tolerances or sizes are rion Any for dimension, part acceptance specification, or rejection. or note that is noted should not be used as a crite- REF Estimating of American Key Standard and Spline involute Sizes splines and required Lengths. Fig. to transmit 1 may a given be used torque. to estimate It also the may size used to find the outside diameter of shafts used with single keys. After the size of the shaft be is found, the proportions of the key can be determined from Table 1 on page2342. splines, Curve lengths A is for are flexible generally splines made with equal teeth to or hardened somewhat to greater Rockwell than C the pitch For diameter these for diameters below 11 4 inches; on larger diameters, the length is generally one-third to two-thirds pling, the length the pitch of the diameter. key being Curve one to A one also and applies one-quarter for a single times key the used shaft as diameter. a fixed cou- stress in the shaft, neglecting stress concentration at the keyway, is about 7500 pounds The square inch. See also Effect of Keyways on Shaft Strength starting on page283. per pounds Curve per B represents square inch, high-capacity neglecting stress single concentration. keys used as fixed Key-length couplings is one for stresses to one and of 9500 quarter times shaft diameter and both shaft and key are of moderately hard heat-treated one-

16 INVOLUTE SPLINES 2141 motor steel. This or generator type of connection shafts. is commonly used to key commercial flexible couplings to quarter Curve times C is for pitch multiple-key diameter and fixed shaft splines hardness with of lengths of three-quarters BHN. to one and oneter. Curve Hardnesses D is for up high-capacity to Rockwell splines C 58 are with common lengths and one-half in aircraft to one applications times the pitch the shaft diame- generally hollow to reduce weight. is low Curve shafts E represents with inside a solid diameter shaft equal with 65,000 to three-quarters pounds per of square the outside inch shear diameter stress. the For shear hol- stress would be 95,000 pounds per square inch. the Length same of shear Splines: strength Fixed as splines the shaft, with assuming lengths of uniform one-third loading the pitch of the diameter teeth; however, will have errors anced in strength spacing of of teeth teeth and result shaft in only the length half the should teeth being be two-thirds fully loaded. the Therefore, pitch diameter. for bal- weight is not important, however, this may be increased to equal the pitch diameter. In the If is case misalignment of flexible splines, to be accommodated. long lengths do Maximum not contribute effective to load length carrying for flexible capacity splines when there be approximated from Fig. 2. may Formulas of 30-degree for involute Torque splines Capacity given of in Involute the following Splines. The paragraphs formulas are derived for torque largely capacity article When Splines Need Stress from an 23, by D. W. Dudley, Product Engineering, Dec. Control ing In additions: the formulas that follow the symbols used are as defined on page2130 with the follow- Dh = inside diameter of hollow shaft, inches; Ka = application factor from Table 1;Km = load distribution factor from Table 2;Kf = fatigue life factor from Table = wear life factor from Table 3;Kw 4;Le = maximum effective length from Fig. 2, to be used in pound-inches. stress formulas For even fixed though splines the without actual helix length modification, may be greater; the effective T = transmitted length torque, Le should never exceed 5000 D3.5 T. Table 1. Spline Application Factors, Ka Type of Load Uniform Power Source (Generator- Shock Light Intermittent Fan) Pumps, (Oscillating Shock Heavy etc.) Pumps, (Actuating Shock etc.) Shears, (Punches, etc.) Application Factor, Ka Uniform (Turbine, Motor) Light Motor) Shock (Hydraulic Medium Combustion, Shock Engine) (Internal

17 2142 INVOLUTE SPLINES Table 2. Load Distribution Factors, Km, for Misalignment of Flexible Splines Load Distribution Factor, Km Misalignment, 1 a inches per inch 2-in. Width Face 1-in. Width Face 2-in. Width Face 4-in. Width Face afor For fixed fixed splines, splines, Km=1. Km = 1. Table 3. Fatigue-Life Factors, Kf, for Splines No. of Torque Fatigue-Life Factor, Kf Cyclesa Unidirectional Fully-reversed 1, , , ,000, ,000, aa torque cycle consists of one start and one stop, not the number of revolutions. Table 4. Wear Life Factors, Kw, for Flexible Splines Revolutions Number of of Spline Life Factor, Revolutions Number of Kw of Spline Life Factor, Kw 10, ,000, , ,000,000, ,000, ,000,000, ,000, olutions Wear life of the factors, spline, unlike since fatigue each revolution life factors of given a flexible in Table spline 3, results are based in a on complete the total cycle number of rocking of rev- motion which contributes to spline wear. with Definitions: rings at each Afixed end spline to prevent is one rocking which is of either the spline shrink which fitted results or loosely in small fitted axial but piloted ments that cause wear. A flexible spline permits some rocking motion such as occurs move- the shafts are not perfectly aligned. This flexing or rocking motion causes axial movement when and only consequently small angular wear misalignments of the teeth. (less Straight-toothed than 1 deg.) before flexible wear splines becomes can a accommodate lem. For greater amounts of misalignment (up to about 5 deg.), crowned splines serious are preferable to reduce wear and end-loading of the prob- teeth.

18 INVOLUTE SPLINES 2143 Pitch Diameter of Splines or OD of Keyed Shaft, inches A Aircraft flexible or single-key commercial B Single-key, high-capacity C High-capacity fixed ,000 10, ,000 1,000,000 Torque, lb-inches D E Aircraft fixed Limit of spline design (65,000-psi solid shaft) Fig. 1. Chart for Estimating Involute Spline Size Based on Diameter-Torque Relationships 10 Pitch Diameter inches For maximum misalignment For moderate misalignment For flexible splines For fixed splines with helix modification Maximum Effective Length L e, inches Fig. 2. Maximum Effective Length for Fixed and Flexible Splines

19 2144 INVOLUTE SPLINES shear Shear stress Stress induced Under in Roots the shaft of External under the Teeth: root diameter For a transmitted of an external torque spline T, the is: torsional S s = 16TK a πd (1) re 3K for a solid shaft f S s = TD re K a D (2) π re 4 D h 4)K for a hollow shaft ( f The computed stress should not exceed the values in Table 5. Table 5. Allowable Shear Stresses for Splines Hardness Max. Shear Allowable psi Stress, Material Brinell Rockwell C Steel ,000 Steel ,000 Steel ,000 Surface-hardened Steel ,000 Case-hardened Steel ,000 Through-hardened (Aircraft Quality) Steel ,000 for Shear a transmitted Stress at torque the Pitch T is: Diameter of Teeth: The shear stress at the pitch line of the teeth S s = 4TK a K DNL m e tk f (3) ing The errors. factor For of poor 4 in (3) manufacturing assumes that accuracies, only half the change teeth will the factor carry to the 6. load because of spac- The computed stress should not exceed the values in Table 5. splines Compressive are very Stresses much lower on Sides than of for Spline gear Teeth: teeth since Allowable non-uniform compressive load distribution stresses and on misalignment result in unequal load sharing and end loading of the teeth. For flexible splines, S c = 2TK m K DNL a e hk w (4) For fixed splines, S c = 2TK m K 9DNL a e hk f (5) 0.9/P In these and formulas, for fillet root h is splines the depth is 1/P, of engagement approximately. of the teeth, which for flat root splines is 6. The stresses computed from Formulas (4) and (5) should not exceed the values in Table

20 INVOLUTE SPLINES 2145 Table 6. Allowable Compressive Stresses for Splines Max. Allowable Material Hardness Compressive psi Stress, Steel Brinell Rockwell C Straight Crowned 1,500 6,000 Steel ,000 8,000 Steel ,000 12,000 Surface-hardened Steel ,000 16,000 Case-hardened Steel ,000 20,000 stress: Bursting 1) tensile Stresses stress on due Splines: to the Internal radial component splines may of the burst transmitted due to three load; kinds 2) centrifugal of tensile tensile bending stress; of the and teeth. 3) tensile stress due to the tangential force at the pitch line causing Radial load tensile stress, S 1 = Ttan πdt (6) φ 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. Centrifugal tensile stress, S 2 = rpm (7) ( )2 D oi D ri ( 000 ) where Doi = outside diameter of spline sleeve.,, Beam loading tensile stress, S 3 = T D2L (8) e Y splines In this of equation, 30-deg. pressure Y is the Lewis angle a form value factor of Y = obtained 1.5 is a satisfactory from a tooth estimate. layout. The For internal in (8) assumes that only half the teeth are carrying the load. factor 4 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 Splines Material Brinell Hardness Rockwell C Max. Allowable psi Stress, Steel ,000 Steel ,000 Steel ,000 Surface-hardened Steel ,000 Case-hardened Steel ,000 Through-hardened Steel ,000 Crowned splines can Splines accommodate for Large misalignments Misalignments. As of up to about mentioned 5 degrees. on Crowned page2142, splineshave crowned

21 2146 INVOLUTE SPLINES precise considerably alignment. less capacity However, than when straight large splines misalignments of the same exist, size if the both crowned are operating spline with greater capacity. has may American be mated Standard with straight tooth forms internal may members be used of for Standard crowned form. external members so that they 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, should F; always and the be made relief somewhat or crown height greater A than at the one-half ends of the the face teeth. width The multiplied crown height by the A ture tangent of the misalignment angle. For a crown height A, the approximate radius of curva- r2 is F2 8A, and r1 = r2 tan φ, where is the pressure angle of the spline. For a torque T, the compressive stress on φ the teeth is: S c = T DNhr 2 ; and should be less than the value in Table 6. occurs Fretting when Damage cyclic to loading, Splines such and Other as vibration, Machine causes Elements. Fretting two surfaces in intimate is wear contact that undergo small oscillatory motions with respect to each other. During fretting, high points to or leaving asperities minute, of the shallow mating pits surfaces and a powdery adhere to debris. each other In steel and parts small exposed particles to are air, pulled the metallic designation debris oxidizes fretting rapidly and forms a red, rustlike powder or sludge; hence, the coined out, Fretting is mechanical corrosion. that do not oxidize, such in as origin gold, platinum, and has been and observed nonmetallics; in most hence, materials, the corrosion including accompanying fretting of steel parts is a secondary factor. those can Fretting destroy can close occur fits; in the the debris operation may of clog machinery moving subject parts; and to motion fatigue or failure vibration may or be both. accelerated undamaged because material. stress Sites levels for to fretting initiate damage fatigue in include fretted interference parts are much fits; splined, lower than bolted, for It keyed, between pinned, leaves and in leaf riveted springs; joints; friction between clamps; wires small in wire amplitude-of-oscillation rope; flexible shafts and bearings; tubes; and electrical contacts. eliminated, Vibration greater or cyclic clamping loadings force are the may main reduce causes movement of fretting. but, if If not these effective, factors may cannot actuallface worsen hardening the methods damage. may Lubrication be effective, may delay not by the reducing onset of fretting, damage; but hard by plating increasing or sur- be fatigue strength of the material. Plating soft materials having inherent lubricity onto contacting surfaces is effective until the plating wears through. the Involute production Spline parts. Inspection Methods. Spline gages are used for routine inspection of