PSI - Issue 8

Francesca Curà et al. / Procedia Structural Integrity 8 (2018) 204–211 Author name / StructuralIntegrity Procedia 00 (2017) 000 – 000

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2

In recent decades, due to the increase in machines performance, shaft and hub are always designed from both static and fatigue point of view, following traditional approaches (as Dudley (1957) and DIN Standards (2000 2006), based on Niemann et al. (2006). Anyhow, it may be observed that the possibility of failures due to shear stresses for high power transmissions is practically negligible. The causes of spline wear, discussed in detail by Ratsimba et al. (2004), can be summarized as an inability of the coupling to adequately accommodate misalignment between shaft and hub (Curà et al. (2013)), a difficulty in maintaining sufficient lubrication, and a basic susceptibility to the process of fretting. Another cause that makes possible the wear damage is the flexibility of teeth, above all in case of strongly variable torque as in high power transmissions. About this, a recent and very interesting study has been carried on by Guo and al. (2013) related to wind turbine gearboxes, leading to understanding the behavior of spline connections and providing recommendations to improve design standards. The torsional stiffness of teeth has also to be carefully taken into account, related not only to its geometry, but also to the applied load, as point out by Wang and al. (2004). An exhaustive study about wear problems in spline couplings necessarily passes through an experimental activity, leading to a comparison between these two kinds of surface damaging, due respectively to angular misalignments and variable amplitude torques, in terms of component durability. The need arises in this regards to realize test specimens that may globally represent the actual working conditions of the real components and that may also predict an eventual disallowance of a transmission. Aim of this paper is to develop a new methodology in order to design a representative test specimen for wear damage characterisation in spline couplings. The present work may be considered as a basis for understanding and predicting fretting wear phenomena in spline couplings from the damage entity point of view. In other words, real component and test specimen (same material) have been considered having a common target that is an isodamage condition reached after an established number of working (testing) cycles. Influence parameters chosen for this aim are, under the hypothesis of equal friction coefficient, the hertzian pressure due to the load entity (torque) and the corresponding slidings. As mentioned before, slidings have been determined referring to two different working conditions, traditional fatigue testing with variable torque (aligned conditions) and wear testing in misaligned conditions. Specimen geometry has been firstly stated following DIN 5480 requirements, then profile micro geometries have been varied to tune the established target parameters; then, the corresponding FEM simulations have been carried on. Hertzian pressure values and corresponding contact areas (extension, shape and position along the face width and respect to the involute profile) have been verified by the classical formula and by FE results. A preliminary experimental activity has been done in order to verify the specimen design related to isodamage dimensioning aspects. Wear tests have been carried on by a dedicated test rig (Cuffaro et al. (2014)) and fatigue tests have been performed by means of a special device connected to a standard fatigue machine (Curà et al. (2017)). 2. Materials and methods

2.1 Geometrical model and analytical calculations

At the beginning of the analysis, spline coupling geometry has been chosen according to DIN 5480-1 (modulus m=3, reference diameter d B =50 mm). The basic rock profile is shown in Figure1. All representative parameters of the spline coupling in its basis configuration are reported in Table 1.

Table 1. Spline coupling parameters (1: shaft, 2: hub. All dimensions in mm). Number of teeth Addendum modification coefficient Reference circle diameter Base diameter Tip circle diameter Root circle diameter

Root form circle d Ff2min 49.47

Tip circle diameter

Root circle diameter

Base form circle diameter

Nominal tooth thickness

Nominal space with

Z

x 1 = -x 2

D

d b

d a2

d f2 50

d a1

d f1

d Ff1max 43.93

s 1

e 2

15

0.28

45

38.97

44

49.40

43.40

5.69

5.69

Then, in order to design a test specimen representative of the actual fretting wear damage due to both misaligned