Theoretical and experimental investigation of wear in internal gears

doi:10.1016/j.wear.2013.11.016

Wear

Volume 309, Issues 1–2, 15 January 2014, Pages 208-215

https://doi.org/10.1016/j.wear.2013.11.016 Get rights and content

Highlights

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Wear in internal spur gears investigated theoretically.
•
A fatigue and wear test equipment is designed to investigate wear experimentally.
•
It is seen that the theoretical and experimental results are compatible.
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In internal gears maximal wear depth occurs in the region of tooth tip.

Abstract

Internal gears are commonly used in automotive and aeronautic industries as external sun gears of planetary mechanisms. Internal gears have some advantages such as low sliding velocities, low contact stresses, high contact ratios compared with external gears. Therefore, manufacturing is more difficult than external gears. For this reason, it is necessary to determine the working conditions of internal gears carefully. For that purpose, wear in internal gears is investigated theoretically by adapting Archard's wear equation to internal gears and a MATLAB^® programme is written to solve this modified equation. The aim is to determine the wear values in different conditions by using this modified equation. In addition, a fatigue and wear test equipment is designed and manufactured which is similar to FZG (Forschungsstelle für Zahnrader und Getreibbau) closed circuit power circulation system in working principle to investigate wear in internal gears experimentally. Internal spur gears which are manufactured from St50 are used in the experiments with different torques and motor speeds. Wear is determined that occurs in tooth profiles of internal gears for different load cycles. It is seen that the results obtained from theoretical and experimental studies are compatible.

Introduction

Internal gears differ from external gears in that their teeth are directed to the interior of gear center. An internal gear mechanism meshes on concave and convex surfaces. Thus, internal gears have advantages of low contact stresses, high contact ratios and low sliding velocities when compared with external gears [1]. Internal gears are widely used in gear boxes as in planetary mechanisms, transmission boxes, and differential mechanisms, in cranes, automotive and aeronautic industries [2]. Researchers are usually investigating gear geometry and tooth fillet stresses with the internal gears.

Some programs are developed for determining the geometry of internal gears to simplify the manufacturing of gears [3], [4], [5]. With the help of these programs, optimized internal gears can be manufactured that are appropriate for working conditions by changing the geometry of the gear (kinematic limits, minimizing center distance or gear volume) easily. These programs are based on theoretical calculations and are not supported with experimental data's. In studies about the optimization of rim thicknesses on internal gears [6], [7], [8], the effects of rim thickness on the tensile and compressive stresses in tooth root are determined. The location and magnitude of maximum tangential stress are aimed to determine in studies for calculating stresses occurring in tooth root of internal gears [9], [10], [11], [12]. Finite element method is used for calculating stresses theoretically and experimental measurements are carried out with strain gages and photo-elastic tests.

Wear is the most common failure type in the working surfaces of mechanical systems. It occurs with the breakage of small particles from both surfaces which are in contact and meshing with each other [2]. Wear is commonly seen in gear mechanisms. Mathematical modeling of wear is firstly suggested by Archard [13]. Afterwards, these formulas are used by Flodin and Andersson [14], [15], [16], [17], [18], [19] to determine wear theoretically in various external gear mechanisms. The aim of this study is to investigate wear theoretically and experimentally in internal gears along line of action in different working conditions.

Section snippets

Wear model in internal gears

In this study, the wear model which is described by Archard [13] and adapted to external gears by Flodin [14] is used by arranging it for internal gears. This model is based on single point observation method [16]. The teeth of mating gear pairs make sliding and rolling motions. As a result of these motions, wear occurs in meshing surfaces. The most used wear model is Archard's wear equation; $\frac{V}{s} = K \frac{W}{H}$ where V is the volume of worn material, s is the sliding distance between contacting surfaces, K

Test gears

The pinion and internal gear which were used in experimental studies were St50 steel with a surface hardness of 160–170 HB (Fig. 4). The geometrical properties of gears are given in Table 1. In Table 1 subscript 1 and 2 shows the pinion and the internal gear respectively.

Test apparatus

For experimental studies, a pinion-internal gear fatigue and wear test apparatus which has the same working principle with FZG closed circuit power circulation system [23], [24] is manufactured and wear experiments are performed

Sliding velocity and contact pressure distributions along the meshing line

Gears are rotated at three different motor speeds (1000 rpm, 1500 rpm, and 2000 rpm) and three different torsional moments (50 N m, 100 N m and 150 N m) to investigate wear along the line of action in internal gears. The effect of sliding velocity and surface pressure along the meshing line is given in Fig. 8, Fig. 9.

Sliding velocity takes different values along the line of action in Fig. 8. Sliding velocities increase along the tip and root of the internal gear and maximum sliding velocity values are

Conclusions

The variation of wear depth along the line of action in internal gears was investigated theoretically and experimentally. Both sets of results indicate that in internal gears, the maximum wear occurs in the region of the tooth tip where the internal gear begins to mesh with the pinion teeth. Accordingly, the critical region for wear in conjugate internal gear-pinion couples is at the tooth tip. An equation which gives the wear depth in internal gears is presented, and a program in MATLAB^® was

Acknowledgements

The authors would like to thank Dr. Sören Andersson for his help during the work. This work is supported by Gazi University Scientific Research Projects (06/2009-06).

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Theoretical and experimental investigation of wear in internal gears

Highlights

Abstract

Introduction

Section snippets

Wear model in internal gears

Test gears

Test apparatus

Sliding velocity and contact pressure distributions along the meshing line

Conclusions

Acknowledgements

Int. J. Mach. Tools Manufact.

Int. J. Mach. Tools Manufact.

Wear

Wear

Wear

Wear

Wear

Wear

Study on friction loss of internal gear drives

JSME Int. J. Ser. III

Teeth of internal gears

J. Franklin Inst.

Bending stresses of internal spur gear

Bull. JSME