**8. Nomenclature**



**8. Nomenclature** 

The prototypes developed operated in stable conditions in the speed range expected. Future

*J*G transverse rotor moment of inertia, calculated respect to the centre of mass

*n,m* number of nodes along axial and circumferential directions

*Re* Reynolds number calculated at supply port section, *Re*=4*G*/(π*d*s*μ*)

investigations will verify the stability at higher speeds.

*c*<sup>d</sup> supply hole discharge coefficient *cOR* damping coefficient of the O-ring

*F*<sup>t</sup> external axial force on thrust bearing

*G* air mass flow rate through the supply hole

*h0* clearance with rotor in centred position

*J*P polar moment of inertia of rotor *k*<sup>T</sup> temperature coefficient*, k*T=ඥʹͻ͵Ȁܶ *kOR* stiffness coefficient of the O-ring

*q* inlet mass flow rate per unit surface

*R*<sup>0</sup> gas constant, in calculations *R*0=287.6 m2/s2K

*T*<sup>0</sup> absolute temperature, in calculations *T*0=288 K *u,v* mean velocity components in *z*- and *θ*-direction

*zF* axial coordinate of the external force on the rotor

*Re*\* modified Reynolds number, *Re*\*=ρω*h*02/*μ*

*c*<sup>s</sup> supply hole conductance *D* journal bearing diameter *d*<sup>s</sup> supply hole diameter

*Fx ,Fy* external forces on rotor

*h* local air clearance

*L* bearing axial length *mb* bushing mass *mr* rotor mass

*p*a ambient pressure *p*s bearing supply pressure

*R* journal bearing radius *r,*θ*,z* cylindrical coordinates

*S* supply hole cross section

*zG* center of mass axial coordinate

∆*z* mesh size in axial direction

*χ* dynamic rotor unbalance

∆*θ* mesh size in circumferential direction *Λ* bearing number, *Λ*=6*μ*ω/*p*a·(*D*/2*h*0)2

*x,y,z* cartesian coordinates

*ex, ey* rotor eccentricities

∆*t* time step

*p* pressure

*b* ratio of critical pressure to admission pressure, *b*=0.528


## **Author details**

G. Belforte, F. Colombo, T. Raparelli, A. Trivella and V. Viktorov *Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Italy* 

#### **9. References**


[14] Belforte, G.; Colombo, F.; Raparelli, T.; Trivella, A; Viktorov, V. (2008a). High speed electrospindle running on air bearings: design and experimental verification, *Meccanica*, Vol. 43, pp. 591-600.

**Chapter 7** 

© 2013 Zhu et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Zhu et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**High Temperature Self-Lubricating Materials** 

There is an ongoing need for developing high temperature self-lubricating materials to meet the severe conditions of mechanical systems, such as advanced engines which require increasingly high working temperatures (at 1000 °C or above) and long life [1-7]. However, achieving and maintaining low friction and wear at high temperatures have been very difficult in the past and still are the toughest problems encountered in the field of tribology [8,9]. Yet, the efforts to explore novel high temperature self-lubricating materials possessing favorable frictional property and superior wear resistance abilities have never stopped. As a result, great strides have been made in recent years in the fabrication and diverse utilization of new high temperature self-lubricating materials that are capable of satisfying the multifunctional needs of more advanced mechanical systems [10-15]. The following

It is well known that the friction and wear of metal alloys at high temperatures are controlled by their tribochemically generated oxide films [16-20]. Consequently, on a hard metal substrate-formed lubricating soft oxide layer, with low shear strength, results in considerable wear reduction and sometimes a decrease of friction. Hence the idea is reasonable and feasible that realization of self-lubricating property by in situ oxide formation on sliding surface at high temperatures. Peterson M.B. and Li S.Z. applied this concept to develop high temperature self-lubricating alloys, such as Ni-Cu-Re, Co-Cu-Re, and Fe-Re, by lubrication with naturally occurring oxides during the sliding process [19-23].

Qinling Bi, Shengyu Zhu and Weimin Liu

http://dx.doi.org/10.5772/55645

**1. Introduction** 

Additional information is available at the end of the chapter

tribological issues addressed in this chapter are presented:

ii. Ni matrix high temperature self-lubricating composites

iii. Intermetallics matrix high temperature self-lubricating composites iv. Ceramic matrix high temperature self-lubricating composites

i. High temperature self-lubricating alloys

v. High temperature self-lubricating coatings.

**2. High temperature self-lubricating alloys** 

