Equivalent Line Contact Research Articles

The Transient Effects of Profile Modification on Elastohydrodynamic Oil Films in Helical Gears

This article presents the results of a transient elastohydrodynamic analysis of the conditions at the contact of two pairs of helical gears operating with different gear ratios. The effects of the variation in contact geometry, kinematics, and tooth loading during the meshing cycle are taken into account together with both tip relief and axial crowning profile modifications. The results are compared with analyses under corresponding steady-state conditions for both point contact and equivalent line contact models. The comparisons show that, away from the ends of the contact lines, steady-state conditions can be used effectively to assess the film-forming capabilities of the gears. Conditions at the end of the contact lines are found to be more adverse with significant transient squeeze film effects. The form of tip relief profile adopted is shown to be highly influential in determining the peak contact pressures and thinnest oil films within the contacts. These conditions are experienced at all axial positions on the tooth flanks at the locations of the start of tip relief profile modifications. If the tip relief profile introduces a slope discontinuity to the gear profile, this can cause a significant stress concentration and very poor film-forming behavior.

Film thickness prediction in elastohydrodynamically lubricated elliptical contacts

This paper analyses the minimum and central film thickness evolution of elastohydrodynamically lubricated contacts, from circular to wide elliptical contacts. It is shown that already for moderate ellipticity, the minimum film thickness is found on the centre-line of the contact, rather than in the side lobes as for the circular contact. In such cases, the film thickness can be accurately predicted from an equivalent line contact, defined as the line contact with the same Hertzian pressure, radius of curvature, and speed and oil parameters. In this paper, a formula is presented to predict the central film thickness in elliptical contacts using prediction formulas for the line and circular contacts as limiting cases, and the results of numerical calculations to fit the film thickness variation with ellipticity. The formula gives an accurate prediction of the central film thickness over the entire ellipticity regime.

Analysis of Mixed Lubrication Effects in Simulated Gear Tooth Contacts

The paper presents results obtained using a transient analysis technique for point contact elastohydrodynamic lubrication (EHL) problems based on a formulation that couples the elastic and hydrodynamic equations. Results are presented for transverse ground surfaces in elliptical point contact that show severe film thinning and asperity contact at the transverse limits of the contact area. This thinning is caused by transverse leakage of the lubricant from the contact in the remaining deep valley features between the surfaces. A comparison is also made between the point contact results on the entrainment center line and the equivalent line contact analysis. The extent of asperity contact is shown to be dependent on the Hertzian contact aspect ratio. It is also shown that transverse waviness (superimposed on the roughness) of even relatively small amplitude can lead to large increases in asperity contact rates over all waviness peaks in the contact.

Transient elastohydrodynamic point contact analysis using a new coupled differential deflection method Part 2: Results

The paper presents results obtained using a transient analysis technique for point contact elastohydrodynamic lubrication (EHL) problems based on a formulation that effectively couples the elastic and hydrodynamic equations. Results are presented for transverse ground surfaces in an elliptical contact that show severe film thinning at the transverse limits of the contact area. This thinning is caused by transverse (side) leakage of the lubricant from the contact in the remaining deep valley features. Comparison is made between the elliptical contact results on the entrainment centreline and the equivalent line contact analysis. This confirms the importance of edge effects as a likely cause of film collapse and scuffing failure. The surface profiles used in the analysis are taken from test discs used in scuffing experiments and from gears used in micropitting tests. Side leakage is found to be sufficiently severe to cause microasperity contact in the numerical examples presented. This contact mainly occurs close to the edges of the corresponding Hertzian area and correlates in position with the location at which scuffing is found to first occur in the earlier experiments. Comparisons are made with other numerical results for point contact configurations with sinusoidally varying surface features obtained by Zhu (2000) and considerable differences are seen in the calculated extent of asperity contact. The differences are thought to be due to the simplified treatment of the lubrication equation adopted by Zhu.

Film thickness in elastohydrodynamically lubricated elliptic contacts

A multilevel solver for the circular contact was extended to elliptical contact problems. After verification of its predictions by comparison with results presented in literature, it was used to study the variations of film thickness with varying operating conditions and aspect ratio of the contact ellipse. Detailed computational results are presented and observed tendencies are traced back to the modelling equations. Subsequently it is demonstrated how and when, for contacts with the entrainment directed perpendicular to the major principal axis of the contact ellipse, the pressure and film thickness on the centre-line of the contact can be predicted accurately from an equivalent line contact analysis. Finally, survey graphs of the minimum and the central film thickness are presented and a formula is given that predicts the central film thickness as a function of load and lubricant parameters, and the ratio of reduced radii of curvature of the surfaces. This formula incorporates asymptotic behaviour and as a result it can be applied for all conditions. In particular, its accuracy for contacts with the major principal axis of the contact ellipse perpendicular to the entraining direction is demonstrated in this paper.

The Elastohydrodynamic Lubrication of Heavily Loaded Point Contacts

It is shown that the film thickness in heavily loaded point contacts can be accurately calculated by comparing the inlet and exit zones of the contact with those of an equivalent line contact. The results become increasingly accurate as the extent of the inlet and exit regions is reduced and in the limit yields an exact solution. Even for moderately loaded contacts in which the inlet zone occupies a substantial part of the contact width the results are in close agreement with existing numerical solutions.