Additional aspects of elastohydrodynamic lubrication

An up-to-date review of the varying aspects of elastohydrodynamic lubrication is presented.. Some recent work on elastohydrodynamic lubrication of materials of low elastic modulus as well as on hydrodynamic lubrication is included. Both these topics are applicable for contacts with any ellipticity parameter (ranging from a circular contact to a line contact)

Toroidal membrane vesicles in spherical confinement

We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict under which conditions a topology change is favored energetically.Comment: 16 pages, 7 figure

Simplified solution for point contact deformation between two elastic solids

A linear-regression by the method of least squares is made on the geometric variables that occur in the equation for point contact deformation. The ellipticity and the complete eliptic integrals of the first and second kind are expressed as a function of the x, y-plane principal radii. The ellipticity was varied from 1 (circular contact) to 10 (a configuration approaching line contact). These simplified equations enable one to calculate easily the point-contact deformation to within 3 percent without resorting to charts or numerical methods

On the Mathematical Simulation of the Measuring of the Intraocular Pressure by Maklakov Method

Maklakov’s method for measurement of the intraocular pressure (IOP) is based on approach, in which an eyeball is modeled as a thin-walled spherical liquid-filled shell. Measuring the IOP one estimates the diameter of the circular contact area of the cornea and the tonometer. In the clinic special tables are used to estimate the IOP relating to the measured diameter. However nowadays the calculating of such tables is based on the empirical values of the IOP. In the present paper the mathematical simulation of the measuring of the intraocular pressure by Maklakov method is considered

Optimum joint profile for constrained motion of a planar rigid-flexible manipulator

Dynamic system performance of a constrained rigid-flexible manipulator in contact with a circular surface is considered here. A dynamic model with zero tip deformation constraint is derived using extended Hamilton’s principle. An analytical approach for vibration of the flexible link using the assumed modes technique is presented. The effect the force exerted at the end-effector and the required joint torque is investigated through the solution of the inverse dynamics problem. Optimum system performance is suggested for the circular contact surfaces considered in this study using the minimum energy criteria for three joint motion profiles

Shakedown analysis for rolling and sliding contact problems

There is a range of problems where repeated rolling or sliding contact occurs. For such problems shakedown and limit analyses provides significant advantages over other forms of analysis when a global understanding of deformation behaviour is required. In this paper, a recently developed numerical method. Ponter and Engelhardt (2000) and Chen and Ponter (2001), for 3-D shakedown analyses is used to solve the rolling and sliding point contact problem previously considered by Ponter, Hearle and Johnson (1985) for a moving Herzian contact, with friction, over a half space. The method is an upper bound programming method, the Linear Matching Method, which provides a sequence of reducing upper bounds that converges to the least upper bound associated with a finite element mesh and may be implemented within a standard commercial finite element code. The solutions given in Ponter, Hearle and Johnson (1985) for circular contacts are reproduced and extended to the case when the frictional contact stresses are at an angle to the direction of travel. Solutions for the case where the contact region is elliptic are also given