Experimental procedure for the evaluation of tooth stiffness in spline coupling including angular misalignment

Highlights

• A dedicated spline coupling test rig has been used for experimental tests.

• An original hexapod measuring device has been developed to measure teeth deformation.

• Experimental spline coupling teeth stiffness has been obtained.

• Experimental results have been compared with theoretical and numerical (FEM) ones.

• The effect of angular misalignment on the tooth stiffness has been analysed.

Abstract

Tooth stiffness is a very important parameter in studying both static and dynamic behaviour of spline couplings and gears. Many works concerning tooth stiffness calculation are available in the literature, but experimental results are very rare, above all considering spline couplings. In this work experimental values of spline coupling tooth stiffness have been obtained by means of a special hexapod measuring device. Experimental results have been compared with the corresponding theoretical and numerical ones. Also the effect of angular misalignments between hub and shaft has been investigated in the experimental planning.

Introduction

Spline couplings and gears are mechanical components used in power transmission systems to transfer torque by means of teeth engaging each other.

Tooth stiffness is a very important parameter influencing their behaviour from both static and dynamic point of view ([1], [2], [3], [4], [5]).

As an example, in spline couplings the tooth stiffness may influence both load and pressure distribution along tooth surface [6] and also the corresponding engagement [7].

Many theoretical models are available in the literature for calculating the tooth stiffness of gears and spline couplings [7], [8], [9], [10], [11], [12], [13], [14]; the most common model consists of the tooth considered as a cantilever beam [8] subjected to different types of loading, namely: bending, shear, compression, and adding the contribution of the root deformation [9], [10], [11]; in particular, the effect of the tooth profile [12], pressure angle [13], and load [14] have been emphasised.

On the contrary, experimental results are very rare; only few works are available in the literature about gear tooth experimental stiffness; as an example Amarnath et al. [15] and Yesilyurta et al. [16] measured the stiffness by means of modal testing procedures in order to assess wear in spur gears; Munro et al. [17] used a standard back-to-back test rig to evaluate the stiffness throughout the full length of the normal path of contact and also into the extended contact region when tooth corner contact occurs.

Concerning spline couplings, literature is completely lacking of experimental works about this topic.

As a matter of fact, in the case of spline couplings, the correct approximation of tooth stiffness is a very important parameter when the pressure distribution has to be exactly calculated, as a little difference in the determination of stiffness may cause a significant variation in the pressure map [18].

Due to the fact that all teeth are engaging in the normal torque transmission, optimisation procedures related to spline couplings are devoted to correctly determine, already in the design phase, the correct pressure distribution on the teeth surface in order to avoid fretting wear, generally being one of the most important failure modes of these components, above all in aerospace applications [19].

Moreover, spline coupling stiffness may influence rotor dynamics and stability in aero engines [3].

The object of the present work is the experimental determination of the tooth stiffness of a spline coupling; to this aim, a special test rig and a dedicated hexapodal displacement measuring device [20], [21] have been set up. In particular, the experimental devices (dedicated to the analysis of spline couplings) have an innovative design, being completely new, including the power re-circulating scheme associated with the ability to perform tests in misaligned conditions. Experimental results have been compared to the corresponding obtained by FEM models and analytical approaches. Also the effect of angular misalignment on tooth stiffness has been experimentally investigated. This aspect, is not investigated in the literature, but it is very important because the angular misalignment influence the load distribution on teeth, in terms of pressure distribution, and may cause both undesired fretting wear [22] and additional loads as tilting moments [23].