Tribology in Machine Components

Abstract

Proper tribological practices are extremely important from the view point of reliable and maintenance free operation of machine components. Friction, wear, and lubrication are three main domains of tribology. Proper interfacing among these domains is essential to have a better performance of machine components. Bearings are most critical machine elements which imparts constrained relative motion between two machine components. Bearings either have sliding contact or rolling contact. In the present chapter different types of bearings have been discussed. The main focus of this chapter is on hydrostatic/hybrid fluid-film journal bearings. The components of the hydrostatic/hybrid bearing system that have significant impact on bearing performance have been described. The analysis of fluid-film journal bearings and their performance characteristics parameters have been discussed. The chapter also discusses some current research trends in the design of hydrostatic/hybrid journal bearings. In concluding section the chapter discusses some of the results pertaining to the current issues of research, which needs to be considered for an accurate and realistic design of hydrostatic/hybrid journal bearing system, such as the number of recesses, type of restrictor, shape of recess, influence of turbulence and flexibility, etc.

Exercise

• 1. Write a brief engineering note on the purpose of lubrication in machine component? How a liquid lubricant is better than a solid lubricant?

• 2. Classify different bearing configurations? List the application of rolling contact Bearing?

• 3. Enumerate the advantages of hydrostatic journal bearing over a hydrodynamic journal bearing?

• 4. Describe in brief need of a restrictor in a hydrostatic journal bearing system? Which type of restrictor will you prefer in high variable load?

• 5. Describe the phenomena of whirl and whip in journal bearing system? How these problems could be overcome?

• 6. What are the advantages of recessed journal bearing over non-recessed journal bearing?

• 7. Derive the generalized form of Reynolds equation in nondimensional form by using suitable nondimensional parameter.

• 8. Write a brief engineering note on bearing performance characteristics parameters.

• 9. Explain Elastohydrostatic/Elastohydrodynamic Lubrication phenomenon. How do these affects the performance of a journal bearing?

• 10. What do you mean by the term Nonlinearity of lubricant? How does the nonlinearity of lubricant affect the performance of a journal bearing?

• 11. Explain the phenomenon of turbulence in the fluid-film journal bearing system. Describe different theories for turbulence applicable to journal bearing.

• 12. A capillary compensated hydrostatic journal bearing system has the following parameters-

  Discharge through capillary	4 × 10−5 m3/s
  Length of capillary	10 cm
  viscosity of lubricant	2.18 × 10−3 N-s/m2
  Supply pressure	1.4 MPa
  Recess pressure	0.5 MPa

  Determine the radius of the capillary.

• 13. Determine the value of discharge of the lubricant through an orifice restrictor for an orifice restricted recessed hybrid journal bearing system with the following data.

  Orifice diameter	10 mm
  Coefficient of discharge	0.55
  Density of lubricant	800 Kg/m3
  Supply pressure	0.15 MPa
  Recess pressure	0.06 MPa

• 14. Determine the load carrying capacity and shear stress for a hydrodynamic journal bearing system for the following data.

  Pressure	1 MPa
  Aspect ratio	0.8
  Length of the bearing	1 m
  Clearance	10−3 m
  Viscosity	2.08 × 10−5 N-s/m2
  Speed of journal	1,000 rpm

• 15. Determine the value of the coupling number and characteristics length for the lubricant with the following characteristics.

  Linear viscosity	2.5 × 10−3 N-s/m2
  Spin viscosity	1.2 × 10−3 N-s/m2
  Characteristics coefficients	0.8 × 10−9 N-s

• 16. Compare the value of the turbulent coefficients for the value of Reynolds number Re = 10,000 using Constantinescu theory.

• 17. Derive the expression of critical mass of journal using the Routh’s criterion of Stability.

• 18. Determine the wear zone for a hydrostatic journal bearing system for the values of nondimensional wear depth parameter of 0.25 and 0.5.

Solutions

• 12. Given that

  Q _R = 4 × 10^− 5 m ³/s; l _c = 0.1 m; μ = 2.18 × 10^− 3 Ns/m ²; p _s = 1.4 MPa; p _c = 0.5 MPa

  $$ {Q}_R={K}_c\frac{\left({p}_s-{p}_c\right)}{\mu }=\frac{\pi {d_c}^4}{128{l}_c}\frac{\left({p}_s-{p}_c\right)}{\mu } $$
  $$ 4\times {10}^{-5}=\frac{\pi {d_c}^4}{128\times 0.10}\frac{\left(1.4-0.5\right)\times {10}^6}{2.18\times {10}^{-3}} $$
  $$ {d}_c=7.926\times {10}^{-4}m $$

• 13. Given that

  d₀ = 10 mm; ρ = 800 kg/m³; p _s = 0.15 MPa; p _c = 0.06 MPa

  $$ {Q}_R=\frac{\pi {\psi}_d{d}_0^2}{\sqrt{8\rho }}{\left({p}_s-{p}_c\right)}^{\frac{1}{2}} $$
  $$ {Q}_R=\frac{\pi \times 0.55\times {\left(10\times {10}^{-3}\right)}^2}{\sqrt{8\times 800}}{\left(\left(0.15-0.06\right)\times {10}^6\right)}^{\frac{1}{2}} $$
  $$ \begin{array}{l}=6.4795\times {10}^{-4}{m}^3/ \sec \\ {}\end{array} $$

• 14. Given that

  p = 1 MPa; L/D = 0.8; L = 1 m; C = 10⁻³ m; N = 1,000 rpm;

  $\mu =2.08\times {10}^{-5} Ns/{m}^2$

  Load carrying capacity

  F_o = p. A = p. π L.D= 1 × 10⁶ × π × 1.25 = 3.92699 × 10⁶ N

  Shear stress

  $\begin{array}{l}\tau =\mu \frac{ du}{ dy}=2.08\times {10}^{-5}\times \frac{\pi \times 10000\times 1.25}{60\times {10}^{-3}}\\ {}=13.6135N/{m}^2\end{array}$

• 15. Given that,

  $\mu =2.5\times {10}^{-3}N-s/{m}^2$

  Spin velocity, κ = 1.2 × 10^− 3 N − s/m ²

  ${\gamma}_1=0.8\times {10}^{-9}N-s$

  $N={\left(\frac{\kappa }{2\mu +\kappa}\right)}^{\frac{1}{2}}=0.4399$

  $\overset{.}{l}={\left(\frac{\gamma_1}{4\mu}\right)}^{\frac{1}{2}}=2.828\times {10}^{-4}m=0.2828\kern0.5em mm.$

• 16. Given that,

  $\begin{array}{l}{R}_e=10000\\ {}{G}_{\alpha }=12+0.026{\left({R}_e\right)}^{0.8265}=64.5985\\ {}{G}_{\beta }=12+0.0198{\left({R}_e\right)}^{0.741}=30.2249.\end{array}$

• 18. Given that,

  Sinα = δ _w  − 1 by Dufrane’s abrasive wear model

  $\begin{array}{l} for,{\delta}_w=0.25\\ {} Sin\alpha =0.25-1\\ {}\alpha ={228.59}^0,{311.40}^0\end{array}$

  $\begin{array}{l} for,{\delta}_w=0.50\\ {} Sin\alpha =0.50-1\\ {}\alpha ={210}^0,{330}^0\end{array}$