ANSI B92.1-1996D.December 1957February 1976Involute Splines”Machine DesignMcGraw-HillProduct EngineeringR. J. DragoUnder Elastic MW. Dudley“Calculation of Involute Splines“Design Work Sheet–13th Series”“Rating the Load Capacity of
适用范围
Involute splines offer a compact and weightefficient
means of transferring torque from
one shaft to another, or between a shaft and
a hub. Involute spline tooth dimensions and
tolerances have been standardized by the
Society of Automotive Engineers, American
Society of Mechanical Engineers and others,
and are published in reference [1]. The basic
equations for involute spline tooth stress
calculations assume that spline tooth
loading is uniformly distributed along the
length of the spline tooth. Non-uniform tooth
loading is addressed in some spline load
rating calculations by applying a “load
distribution” factor as in [2] and [3]. Load
distribution factors are used to account for
misalignment (slope) between the internal
and external spline members. The load
distribution factor is influenced by the
magnitude of the misalignment (slope)between the members, and by crowning of
the spline teeth which reduces end-loading
of the spline teeth thereby accommodating
the misalignment.
There is another mechanism that can cause
non-uniform contact loading of spline teeth.
It has been reported in [4], that as the length
of a spline increases relative to its diameter,
the torsional stiffness of the members in the
joint exert a stronger influence on the
lengthwise contact load distribution. This
non-uniform contact load distribution can
occur in perfectly aligned spline joints. The
mechanism is not dependent on angular
misalignment of the member’s axes, but
rather by the relative torsional stiffnesses
and deflections (wind-up) of the internal and
external members. In longer splines, the
tooth contact load peaks near the start of the
joint then falls away toward the end of the
joint [4]. The start of the joint is considered
to be where torque first begins to be
transferred from the inner member to the
outer member, as in a shaft to a hub. In
splined joints where the inner and outer
members have complex geometries (rather
than simple cylindrical geometries) torsional
stiffness can vary non-uniformly along the
length of the joint leading to further nonuniformity
of the tooth contact load
distribution. Indeed, in some splined
members with complex geometries, very stiff
“hard points” may exist that resist torsional
deflection and result in high contact loads
over relatively short tooth lengths. Predicting
tooth contact load distribution for these
situations can be quite difficult.
Figure 1 LMR Rotor Hub and Shaft
(Section of Hub Removed for Clarity)
One application that utilizes a relatively long
splined joint, between a shaft and a hub with
complex geometries, occurs on the CH-47
helicopter. The splined joint in question
transfers torque and rotary motion from the
rotor shaft to the rotor hub. The rotor hub
provides the attachment (via lugs) and load
transfer to the helicopter rotor blades. A
sectioned view of the rotor hub with the mating shaft is shown in Figure 1. The shaft
spline teeth that mate with the hub are split
into two lengths, an upper and lower spline,
with an un-splined cylindrical section
between them as shown in Figure 2.