#ELLIPSE EQUATION CALCULATOR FULL#

Film thickness in elastohydrodynamically lubricated elliptic contacts. Lubrication and beyond, University of Twente lecture notes, 2000. Proceedings of the Royal Society of London. direction of lubricant entrainment coincident with the major axis of the Hertzian contact ellipse. A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. Isothermal elastohydrodynamic lubrication of point contacts. Modified load parameter, , dimensionlessĮllipticity parameter, , dimensionless. For Nijenbanning & Moes equations, the sum velocity is used:, Įquivalent radii of curvature in (X,Y) directions (ellipse), Įffective radius in the direction of lubricant entrainment, Mean entraining velocity, in the equations by Chittenden et al and Hamrock & Dowson. Entraining speed is parallel to the major contact axis of the contact ellipse Definitions: Its important to note here that is defined as a sum velocity: (as opposed to the definition of Chittenden et al, where it is defined as mean entraining velocity)įigure 2.

In this case, equations change as follows: Note, that Chittenden et al also describes the case when the entraining speed is parallel to the major axis of the contact ellipse (see Figure 2). In a standard situation where the entraining speed direction coincide with and is parallel to the minor axis of the contact ellipse (see Figure 1), the minimum film thickness according to Chittenden et al is as follows: Here, the direction is the direction of entraining velocity and is parallel to the minor contact axis of the contact ellipse (see Figure 1, axis ). In practice, this is the most commonly encountered case (e.g., this is the case in bearings). Minimum film thickness formulas Hamrock & Dowson et al formula Įntrainment direction is perpendicular to the major axis of the contact ellipse (see Figure 1, the speed direction is perpendicular to ). Its important to note here that is defined as a sum velocity: (as opposed to the definition of Chittenden et al and Hamrock and Dowson, where it is defined as mean entraining velocity) Thus in the calculator only this standard case is considered. It should be however noted that in practice the entraining speed is parallel to the minor axis of the contact ellipse and all other film thickness fits assumes the standard situation. Parameters are as follows (definition of variables can be found at the end of the article): Dimensionless central film thickness is given by the following equation: Hamrock & Dowson equation was derived assuming that the direction is the direction of entraining velocity and is parallel to the minor contact axis of the contact ellipse (See Figure 1). Central film thickness formulas Hamrock & Dowson formula The calculator allows choosing one of the three equations in the calculations. The equations used in the calculator are given below the calculator along with the definitions and references.

The central and minimum film thicknesses are calculated using equations developed by Hamrock & Dowson, Chittenden et al and Nijenbanning & Moes.

#ELLIPSE EQUATION CALCULATOR FULL#

An EHL Film Thickness Calculator allows calculating central and minimum film thicknesses in a full film lubricated elliptical (point) contact as a function of entrainment speed.

Ellipse equation calculator