CLC number: TH13

On-line Access: 2014-04-03

Received: 2013-09-30

Revision Accepted: 2014-01-10

Crosschecked: 2014-03-17

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Francesca Curà, Andrea Mura. Analysis of a load application point in spline coupling teeth[J]. Journal of Zhejiang University Science A, 2014, 15(4): 302-308.

@article{title="Analysis of a load application point in spline coupling teeth",

author="Francesca Curà, Andrea Mura",

journal="Journal of Zhejiang University Science A",

volume="15",

number="4",

pages="302-308",

year="2014",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.A1300323"

}

%0 Journal Article

%T Analysis of a load application point in spline coupling teeth

%A Francesca Curà

%A Andrea Mura

%J Journal of Zhejiang University SCIENCE A

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%@ 1673-565X

%D 2014

%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.A1300323

TY - JOUR

T1 - Analysis of a load application point in spline coupling teeth

A1 - Francesca Curà

A1 - Andrea Mura

J0 - Journal of Zhejiang University Science A

VL - 15

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SP - 302

EP - 308

%@ 1673-565X

Y1 - 2014

PB - Zhejiang University Press & Springer

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DOI - 10.1631/jzus.A1300323

**Abstract: **The objective of this paper is to investigate the position of the resultant force in involute spline coupling teeth due to the contact pressure distribution for both ideal and misaligned conditions. In general, spline coupling teeth are in contact all along the involute profile and the load is far from uniform along the contact line. Theoretical models available in publications consider the resultant contact force as it is applied at the pitch diameter, and this study aims to evaluate the error introduced within the confines of a common approximation environment. This analysis is carried out through using finite element method (FEM) models, considering spline couplings in both ideal and misaligned conditions. Results show that the differences between the load application diameter and pitch diameter are not very obvious in both ideal and misaligned conditions; however, this approximation becomes more important for the calculation of the tooth stiffness.

**
**

1. Introduction

In both gears and splined coupling teeth (Cornell,

Teeth stiffness is an important parameter in splined couplings when calculating the contact pressure distribution between the teeth (Adey et al.,

In calculating teeth stiffness of spline couplings, many previous studies considered the resultant load as applied on a point of the pitch diameter

Considering splined couplings, the resultant contact force may vary not only due to the pressure distribution along the teeth heights, but also because of possible misalignment conditions, which can cause parallel offsets (Weber,

In this work, the position of the application point of the resultant contact force in the involute spline coupling teeth and the corresponding effects are investigated. This study is carried out by using finite element method (FEM) models, and considers spline couplings in ideal conditions and also with parallel offset misalignments.

2. Calculation of the resultant application point

The coordinates for this center of the area (Fig.

The resultant radius

3. Finite element method models

Fig.

Parameter | Value |

Modulus (mm) | 1.27 |

Number of teeth | 26 |

Pitch diameter (mm) | 33.02 |

Pressure angle (°) | 30 |

Material | Steel |

Elastic modulus (MPa) | 206 000 |

Poisson’s ratio | 0.3 |

The nodes on the hub outer diameter were bounded in all directions, excluding the radial displacement (in this way the radial expansion, due to the radial component of the contact load between teeth, is allowed), and the load was applied on the nodes of the shaft’s inner diameter (Fig.

The contact between the teeth was modelled by means of contact elements.

FEM results provide the load distribution along the teeth height, in terms of contact forces shared between nodes of the engaging teeth. Fig.

The FEM model in nominal conditions was run with five different loading levels: 200, 500, 1000, 3000, and 5000 N·m. FEM models with parallel offset misalignments have been run with three load levels, 200, 1000, and 5000 N·m. Totally, 11 test cases were considered.

4. Results and discussion

Table

Test case | Torque (N·m) | Load application diameter (mm) | Difference (%) |

1 | 200 | 32.78 | 0.74 |

2 | 500 | 32.74 | 0.85 |

3 | 1000 | 32.52 | 1.53 |

4 | 3000 | 32.50 | 1.57 |

5 | 5000 | 32.49 | 1.60 |

Table

When considering spline couplings with a parallel offset error (PO) (this means that the shaft is shifted in the radial direction with respect to the hub), the theoretical pitch diameter

Load application diameters obtained from misaligned models were compared, tooth by tooth, with the theoretical values obtained by Eq. (

Results are shown respectively in Figs.

Fig.

Considering the spline coupling with 0.08 mm parallel offset misalignment, results for the 200 N·m torque are less uniform with respect to the other case; this fact may be due to the high misalignment level that, with a relative low load value, causes an imperfect (not total) contact between teeth. However, in this case, the maximum percentage difference between FEM results and theoretical pitch diameter is 2.94%, obtained with a torque of 200 N·m.

The results presented above show a small difference between the theoretical application point of the resultant force and the actual one. However, by calculating the tooth stiffness with the actual load application point, it is possible to emphasize that this approximation produces a fundamental effect on the tooth stiffness.

In particular, Fig.

It is possible to observe that a small difference in the approximation of the load application point (up to 1.60%) brings about a more important difference related to the tooth stiffness value (up to about 15%) (Fig.

Fig.

5. Conclusions

The investigation was conducted using FEM models. The resultant force application diameter was numerically obtained for a spline coupling in nominal conditions and with parallel offset misalignments. In particular, two levels of parallel offset misalignment were considered (0.02 mm and 0.08 mm). For each case, different loading levels were applied.

Results show that in nominal conditions, the difference between load application diameter and pitch diameter increases with the increase of loading level and the maximum difference is 1.60%. In models with parallel offset misalignment, the maximum difference between FEM results and theoretical pitch diameter is 2.94%, obtained in the case of a 0.08 mm misalignment.

In general, it is possible to point out that the differences between the load application diameter and pitch diameter is not very high in both ideal coupling and with the parallel offset misalignment spline coupling, but this approximation becomes more important if the tooth stiffness is calculated with the actual load application points. In fact, the difference between the stiffness values obtained considering the load applied on the pitch diameter and those obtained with the actual load application point increases to about 15%.

The effect of the load application point variations was evaluated related to the axial pressure distribution, showing that this parameter may also be influenced by the position of the load application point.

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