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Abstract The paper presents a wear model for worm gears that takes into account the pressure and film thickness generated in the elastohydrodynamic oil film that separates the tooth components. Wear is calculated based on the well known Archard wear law applied to each point on the wheel tooth surface. The calculated wear is then used to modify the geometry and the calculation process is repeated in a series of wear steps. Results are presented that show the way in which the wear pattern emerges from the analysis, and that this is generally insensitive to the size of the wear step used.23593
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Keywords: wear model, worm gears, elastohydrodynamic lubrication.
1. INTRODUCTION
Worm gears are possibly unique amongst gear power transmission systems in that the geometry of the load bearing areas of the teeth is changed continuously by wear processes during the lifetime of the gear pair. The configuration adopted for the current study is the most common one for power transmission applications: a steel worm component meshing with a phosphor bronze gear wheel. Gears of this form are usually manufactured with an “oversize” hob which gives a contact that occurs at a point rather than a line under zero load, so as to obtain benefits in lubrication and to avoid contact areas that reach the physical edges of the meshing components. The kinematic action of worm gears ensures that the wheel component is almost stationary relative to the contact point, and the gears essentially operate in a simple sliding mode. As a result, the wheel component is subject to wear due to the sliding action of the worm over its surface. The steel worm also experiences wear but this occurs at a much lower rate than that found in the wheel. The bronze teeth of the wheel are able to sustain this aggressive lubrication regime successfully, and their loss of material due to wear is recognised as an inevitable feature of the configuration. Indeed, the extent to which material has been lost is assessed during maintenance inspections by measuring the increase in backlash, and this change is monitored until its extent indicates that the wheel teeth are becoming too thin to sustain their duty load. During operation of the gears there is an initial period of relatively rapid wear that is usually referred to as bedding in of the gears. During this period the actual contact area of the teeth under load increases so as to reduce the (average) contact stress levels. After bedding in has occurred the gear pair tends to wear at a reasonably steady rate for the remainder of its life cycle. This steady wear rate can be influenced by a number of factors and effectively determines the lifetime of the gear mesh.
The gear surfaces are able to sustain the high levels of sliding to which they are subjected because of elastohydrodynamic lubrication (EHL). This is the lubrication mechanism that protects the contacting surfaces of most gear pairs, but the configuration of worm gears is far from optimal as far as generating lubricant films to separate the surfaces are concerned. The contact area over which the load is carried tends to be a long thin ellipse which is distorted into a banana shape by the enveloping nature of the surfaces. Such a configuration could yield relatively thick lubricant films if lubricant entrainment was in the direction of the minor axis, i.e. across the contact area. Unfortunately, this is not the case as the sweeping action of the worm ensures that entrainment is effectively along the major axis of the contact ellipse. The authors have previously examined the film forming capability of a large number of worm gear designs [1,2] based on a full thermal EHL analysis, and this study identified locations of particularly thin films within the contact area, caused by the unfavourable kinematic action of the gears.
The current paper presents the means by which the EHL film forming analysis has been extended to include a calculation of the wear rate at each point on the wheel tooth surface. This wear pattern is then integrated over the meshing cycle to obtain the tooth wear per wheel rotation. The wear is not uniform and modifies the effective contact area. This effect of wear on wheel tooth geometry is taken into account by recalculating the EHL film and pressure distributions at the end of a series of wear stages and incorporating the calculated change in wheel tooth shape into the subsequent calculations.