A generalized semi-analytical load distribution model for clearance-fit, major-fit, minor-fit, and mismatched splines

Abstract

A generalized semi-analytical load distribution model for all common types of involute spline joints is proposed. It is formulated to model clearance-fit (side-fit) involute splines with contacts happening only at the drive flanks of the spline teeth, major or minor-diameter fit splines where additional contact occurs along the top land and the root land of the external spline teeth, respectively, as well as mismatched splines where an intentional lead mismatch is introduced to initiate contact along both drive and back (coast) flanks. Using this model, load distribution and tooth-to-tooth load sharing of example major and minor diameter-fit spline joints under typical multi-directional spur and helical gear loading conditions are characterized and compared to those of the corresponding side-fit spline joint. Further, self-centralizing performance of major and minor-fit splines versus side-fit splines is quantified including its sensitivity to the radial clearance magnitude. Finally, load distribution of an example side-fit spline having various intentional mismatch magnitudes at different torque level is investigated to show that a given mismatch value is optimal at a certain design torque.

An Experimental Investigation of the Load Distribution of Splined Joints Under Gear Loading Conditions

“…While the studies by Hong et al [1,[10][11][12] indicate that their proposed method is advantageous in capturing key effects and providing computationally efficient analyses, it lacks experimental validation; so do the other models cited previously. The literature contains several experimental studies on splined joints investigating surface wear and fatigue.…”

“…In Figure 1.1(b), a major-fit spline is shown with additional contact along the major diameter of the spline. Finally, in Figure 1.1(c), a minor-fit spline is shown that has additional contact along the minor diameter of the spline [1]. In major and minor diameter-fit splines, there is often a circumferential clearance such that the torque is carried by one side of the tooth flanks while the contact along the major or minor diameter centers the components.…”

“…This torsional loading results in an axisymmetric load distribution where all teeth have the same load distribution. A recent study by Hong et al [1,[10][11][12] produced a family of analytical models which significantly surpassed the capabilities of the previous models. As shown in Figure 1.3, the clearance-fit spline model of Hong et al [10] considers the regions of contact on each tooth of the splined joint from the start of active profile (SAP) to end of active profile (EAP) of the external spline.…”

“…Hong et al [1] later expanded their clearance-fit model to include major and minor diameter-fit spline simulations. Furthermore, they studied the influence of index errors on the resultant load distributions [11].…”

An experimental investigation of the load distribution of splined joints under gear loading conditions

“…Building on the results of their earlier FE study, Hong et al Benatar, Talbot and Kahraman, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.6 (2017) (2014b, 2015a, 2015b) published a family of semi-analytical models which both reduced the computational time immensely and surpassed the capabilities of the previous models which were mostly limited to purely torsional loading. These models captured the impact of loading type (purely torsional, spur, or helical gear loading) on the resultant load distribution of the joint for clearance-fit (Hong, et al, 2014a) as well as major and minor diameter-fit splines (Hong, et al, 2015a). The models also displayed the influence of index errors on the resultant load distributions of a splined joint (Hong et al, 2015b).…”