Starvation

Tags Wiki: #EHD , #lubricant , #lubrication , #lubrication regime , #starvation .

Starvation describes lubricant starvation as a practical tribology topic: how surfaces interact, how friction, wear, lubrication, material response, and operating environment influence performance, and what engineers should check when applying the concept in real machines or laboratory tests.

Core idea: lubricant starvation should be interpreted as a system-level contact problem, not as an isolated material property.
Engineering relevance: load, speed, temperature, surface roughness, chemistry, and lubrication regime can change the observed behavior.
Good practice: combine measurements with surface inspection and clear reporting of test conditions.
Failure prevention: use the topic to identify risks early, compare alternatives, and improve reliability.

What is Starvation?

Starvation is part of the wider study of friction, wear, contact mechanics, materials, and lubrication. In practical use, the term is most useful when it is connected to a defined contact pair, surface condition, operating load, motion type, and environment.

For engineers, lubricant starvation is not only a definition. It is a way to ask which mechanisms control performance at an interface: elastic or plastic deformation, adhesion, abrasion, fatigue, chemical film formation, lubricant starvation, debris generation, or changes in surface topography.

Why Starvation matters in tribology

Starvation matters because small changes at the surface can produce large changes in efficiency, temperature, noise, lifetime, and failure risk. A contact that appears acceptable under one load, speed, or lubricant can behave very differently when the regime shifts from full-film lubrication to mixed or boundary lubrication.

Question	Why it matters
What materials and surfaces are in contact?	Hardness, roughness, coating, oxide layers, and chemistry influence friction and wear.
What motion occurs?	Sliding, rolling, reciprocating, impact, and vibration activate different damage mechanisms.
What lubrication regime is present?	Boundary, mixed, hydrodynamic, and elastohydrodynamic regimes produce different surface separation and film behavior.
What environment is involved?	Temperature, humidity, vacuum, contamination, and reactive species can strongly change tribochemical response.

Engineering factors to consider

Contact stress and geometry: estimate nominal and local contact pressure, including asperity-scale effects where relevant.
Surface topography: measure roughness, waviness, texture direction, and surface defects before and after testing.
Lubricant selection: consider viscosity, additives, supply method, contamination, and compatibility with materials.
Thermal conditions: frictional heating can change viscosity, hardness, oxidation rate, and tribofilm formation.
Running-in: early surface adaptation may control the later steady-state response.
Debris control: wear particles can become a third body, accelerating abrasion or changing friction.

Measurement and interpretation

When evaluating lubricant starvation, report the test configuration clearly: specimen geometry, material grade, surface roughness, lubricant, load, speed, temperature, duration, environment, and repeat count. Tribology results are often system-dependent, so a coefficient of friction, wear scar, or lifetime result should not be treated as a universal property without context.

Useful measurements include friction trace, wear volume or wear rate, surface profilometry, optical or electron microscopy, hardness, lubricant condition, and chemical surface analysis where tribofilms or oxidation are expected.

Detailed background and source material

It is said that a contact operates under “starvation conditions” when an increase of oil supply at the contact would result in an increase of the film thickness at the contact. In other words, when the availability of the lubricant is limited and hence determines the lubriaction regime at the contact (1).

Starvation Model of Kingsbury

In a “starved” bearing, the oil on the track is about as thick outside the contact as in it. Stroboscopic observation of interference fringes confirms that such thin films flow very slowly in the centrifugal fields due to the bearing rotation. The working oil is thus stationary with respect to the track outside the contact, and remains unloaded most of the time. The oil within the contact may flow in the direction of rolling and also across of it. Its viscosity might singificantly increase due to the high pressure. The flow in the rolling direction cannot vary the average film thickness since it does not remove any oil from the track. Only the transverse oil flow can change the overall film thickness. The long-term decay in film thickness observed with oil jags in starved EHD contact, thus imply that transverse oil flowing out of the Hertzian contact area must be considered.

Schematic representation of a starved EHL contact. The dashed area corresponds to the Hertzian contact area.

From the Reynolds equation (see equation 5) the speed of the flow perpendicular to the rolling direction is known:

(1) $\begin{eqnarray*} \omega = \frac{1}{2\mu}\frac{\partial p}{\partial z}(y^2-yh) \\ \end{eqnarray*}$

To calculate the flow out from the contact, it is necessary to integrate the speed of flow in the direction of rolling/sliding and across the film thickness:

(2) $\begin{eqnarray*} Q_{out} = \int_{-a_h}^{a_h} \int_{0}^{h} \frac{1}{2\mu}\frac{\partial p}{\partial z}(y^2-yh) dy dx = \frac{a_h h^3}{6\mu}\frac{\partial p}{\partial z} \\ \end{eqnarray*}$

The term $\frac{\partial p}{\partial z}$ is approximated as $\frac{P_m^h}{b_h}$ and $P_m^h$ is the mean Hertz pressure. Thus, the flow rate out of the contact in the direction perpendicular to rolling/sliding can be written as follows:

(3) $\begin{eqnarray*} Q_{out} = \frac{a_h h^3}{6\mu}\frac{P_m^h}{b_h} \\ \end{eqnarray*}$

This equation gives the amount of liquid flow out from the Hertzian contact for the given film thickness $h$ .

The flow in the rolling/sliding direction is neglected in the model, since in the starved EHL contacts the film thickness outside the contact is the same as inside and therefore the average flow in this direction must be cancelled.

Any change in the volume of the lubricant (film thickness) in time, i.e., flowrate, has to be balanced by $Q_{out}$ :

(4) $\begin{eqnarray*} dV = 2a_hb_hdh=-Q_{out}dt=-\frac{a_h h^3}{6\mu}\frac{P_m^h}{b_h} \\ \end{eqnarray*}$

Hence,

(5) $\begin{eqnarray*} \frac{ 12\mu b_h^2}{P_m^h} \frac{dh}{h^3} = -dt \\ \end{eqnarray*}$

Integration of both sides of this equation gives:

(6) $\begin{eqnarray*} -\frac{6\mu b_h^2}{P_m^h} \frac{1}{h^2} = -t + C \\ \end{eqnarray*}$

where $C$ is a constant. This constant can be obtained from the initial condition: $t=0, h = h_0$ . Finally, the equation gets the following form:

(7) $\begin{eqnarray*} \frac{h_0^2}{h^2} = \frac{P_m^h h_0^2 t}{ 6\mu b_h^2} + 1\\ \end{eqnarray*}$

Rearranging this equation gives:

(8) $\begin{eqnarray*} \frac{h}{h_0} = {(\frac{P_m^h h_0^2 t}{ 6\mu b_h^2} + 1)}^{-1/2}\\ \end{eqnarray*}$

Using this equation one can find the amount of oil that flows out of the contact for the given time $t$ . This equation can be applied to the case of bearings or multiple passages of a ball or a sphere on the same spot of the disk. To do so, we can take the time $t$ as $t=nT$ , where $n$ is the number of passages and $T$ is the period of time between two passages. Then our equation becomes:

(9) $\begin{eqnarray*} \frac{h}{h_0} = {(\frac{P_m^h h_0^2 n}{ 6\mu b_h^2} T + 1)}^{-1/2}\\ \end{eqnarray*}$

In this last form the equation allows one to calculate readily the loss of lubricant from the contact after several passages of a ball or sphere through the contact zone. It should be mentioned that this model assumes no reflow of oil back to the contact, which is quite unrealistic from most of the practical problems. In reality, once the oil has left the contact, it is forced to flow back int it by surface tension driven flows.

Chevalier/Damiens Starvation Model

The approach of Kingsbury was further generalized by Chevalier and Damiens (2,3). By performing a large number of numerical and experimental work, they found that the folowing model can be used to describe the outflow of oil from the contact:

(10) $\begin{eqnarray*} Q_{out} = \alpha h^{\gamma + 1} \\ \end{eqnarray*}$

Following the same approach as in Kingsbury model, one can get the following expression for the film thickness:

(11) $\begin{eqnarray*} \frac{1}{\gamma h^\gamma} = \alpha' t + C \\ \end{eqnarray*}$

where $C$ is the integration constant. If now $t=nT$ and the initial oil level at $n=0$ is $h_{oil}$ , then $C=\frac{1}{\gamma h_{oil}^{\gamma}}$ and hence:

(12) $\begin{eqnarray*} \frac{1}{\gamma h^\gamma} = \alpha' T + \frac{1}{\gamma h_{oil}^{\gamma}} \\ \end{eqnarray*}$

FAQs

What is Starvation in simple terms?

Starvation is a tribology topic used to understand how contacting surfaces behave under load, motion, lubrication, and environmental conditions.

Why is lubricant starvation important for engineers?

It helps engineers diagnose friction and wear problems, choose materials or lubricants, design tests, and prevent surface-related failures.

How should lubricant starvation be tested?

Testing should reproduce the relevant contact geometry, motion, load, speed, temperature, surface roughness, lubricant, and environment as closely as practical.

What should be reported with lubricant starvation results?

Report materials, roughness, lubricant, load, speed, temperature, duration, environment, friction history, wear measurement method, and post-test surface observations.

References and further reading

Bhushan, B. Introduction to Tribology. Wiley.
Stachowiak, G. W., and Batchelor, A. W. Engineering Tribology. Butterworth-Heinemann.
Hamrock, B. J., Schmid, S. R., and Jacobson, B. O. Fundamentals of Fluid Film Lubrication. CRC Press.
NIST resources for measurement, materials, and surface characterization.

Last updated: May 2026. Reviewed topic: Starvation, tribological performance, measurement, and failure prevention.