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**Fluid film lubrication: Theory and design.**
*(English)*
Zbl 1001.76001

Cambridge: Cambridge University Press. xi, 414 p. (1998).

The book is divided into 11 chapters. Chapter 1 gives a brief historical accound of the development of lubrication theories. It is shown that a machined surface always consists of asperities and valleys (when scanned with electron microscope or optical interferometer). How such a surface can be described mathematically, is also explained. Then the author introduces the concepts of friction, lubrication and wear. Tables give experimental details of static and dynamic friction for various surface pairs under dry and greasy conditions. Besides, many other details are given which could be useful to theoretical workers.

In chapter 2, the basic Navier-Stokes equations of motion of Newtonian fluid are derived (fluid is considered as a continuum) and, using lubrication approximation, the Navier-Stokes equations are simplified. This results in a set of nonlinear equations of lubrication theory which include fluid inertia effects. This derivation is novel. These equations are further simplified by assuming that the Reynolds number of fluid film is small, and classical Reynolds equations of lubrication theory are obtained. These equations are linear, and they are integrated for hydrostatic thrust bearing, for slider bearing, and for journal bearing. The theoretical results are compared with experimental results. Both long and short journal bearings are discussed, and the occurrence of cavitation in the fluid film is mentioned. The rest of this chapter is devoted to the discussion of different boundary conditions (Sommerfeld and Swift-Stieber boundary conditions).

In the remaining chapters, the reader can find the discussion of the effects of fluid intertia under the following conditions: (i) when temporal variations of velocity are important (the equations of lubrication theory are linear); (ii) the convective inertia terms are important (the motion is steady and the equations are quasilinear); (iii) the total inertia is important (the motion is unsteady and the equations of the lubrication theory are quasilinear). The methods of finding solutions in all the cases are presented. Further, the author describes elastohydrodynamic lubrication, thermal and turbulence effects, non-Newtonian lubricants and gas lubrication which involve variation of viscosity with temperature, and finally the solution of energy equation related to the lubrication equation.

The book is recommended to research engineers, research applied mathematicians, and to all good libraries. I also hope that this book will stimulate the collaboration between engineers and applied mathematicians in the development of lubrication theory.

In chapter 2, the basic Navier-Stokes equations of motion of Newtonian fluid are derived (fluid is considered as a continuum) and, using lubrication approximation, the Navier-Stokes equations are simplified. This results in a set of nonlinear equations of lubrication theory which include fluid inertia effects. This derivation is novel. These equations are further simplified by assuming that the Reynolds number of fluid film is small, and classical Reynolds equations of lubrication theory are obtained. These equations are linear, and they are integrated for hydrostatic thrust bearing, for slider bearing, and for journal bearing. The theoretical results are compared with experimental results. Both long and short journal bearings are discussed, and the occurrence of cavitation in the fluid film is mentioned. The rest of this chapter is devoted to the discussion of different boundary conditions (Sommerfeld and Swift-Stieber boundary conditions).

In the remaining chapters, the reader can find the discussion of the effects of fluid intertia under the following conditions: (i) when temporal variations of velocity are important (the equations of lubrication theory are linear); (ii) the convective inertia terms are important (the motion is steady and the equations are quasilinear); (iii) the total inertia is important (the motion is unsteady and the equations of the lubrication theory are quasilinear). The methods of finding solutions in all the cases are presented. Further, the author describes elastohydrodynamic lubrication, thermal and turbulence effects, non-Newtonian lubricants and gas lubrication which involve variation of viscosity with temperature, and finally the solution of energy equation related to the lubrication equation.

The book is recommended to research engineers, research applied mathematicians, and to all good libraries. I also hope that this book will stimulate the collaboration between engineers and applied mathematicians in the development of lubrication theory.

Reviewer: R.Usha (Chennai)

### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76D08 | Lubrication theory |