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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.
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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.
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