7. Hydrodynamic and Hydrostatic Lubrication

Introduction and Context

Lubrication separates two surfaces in relative motion and thereby controls friction, wear, temperature, noise, and reliability. In advanced tribological systems, the lubricant is not merely a passive film-forming material. Its pressure distribution, viscosity, inertia, thermal state, and supply conditions determine whether a bearing can support load without destructive contact. Hydrodynamic and hydrostatic lubrication are two major forms of fluid-film lubrication used in turbines, compressors, pumps, machine tools, engines, precision stages, and high-speed rotating machinery.

In hydrodynamic lubrication, the relative motion of the surfaces drags lubricant into a converging clearance and generates pressure within the film. No externally pressurized supply is essential for load generation. In hydrostatic lubrication, an external pump supplies lubricant under pressure, allowing a load-carrying film to exist even when the surfaces are stationary or moving slowly. Hybrid bearings combine both mechanisms.

The central analytical model is the Reynolds equation, obtained by reducing the Navier–Stokes equations using assumptions appropriate to thin lubricant films. Its solutions provide pressure, load capacity, flow rate, friction, and film-thickness information. However, a useful bearing analysis must also account for cavitation, thermal effects, leakage, stability, manufacturing tolerances, and the reliability of the oil-supply system.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Explain the physical mechanisms of hydrodynamic, hydrostatic, and hybrid lubrication.

2. Derive the Reynolds equation from simplified fluid-flow equations.

3. Select suitable assumptions and boundary conditions for journal, thrust, and slider bearings.

4. Estimate pressure, load capacity, friction, flow, and power loss using analytical models.

5. Explain cavitation, rupture and reformation boundaries, and mass-conserving conditions.

6. Evaluate hydrostatic bearing restrictors, stiffness, leakage, and pump requirements.

7. Assess thermal, stability, manufacturing, and operational limitations.

8. Apply bearing theory to engineering design and interpret numerical or experimental results.

The Physical Basis of Fluid-Film Load Support

Consider two surfaces separated by a lubricant film of local thickness h. If one surface moves relative to the other and the film is converging in the direction of motion, viscous drag carries lubricant into a narrowing wedge. Continuity requires the average velocity to increase or decrease in response to the changing gap. The resulting pressure gradient can support an externally applied load.

A parallel film does not normally generate hydrodynamic pressure in a steady, incompressible, isoviscous situation. A converging geometry, such as that of a tilted slider or an eccentric journal, is necessary. Pressure is generated because the moving surface entrains more lubricant than can pass through the narrow region without a pressure-driven counterflow.

Hydrodynamic action is self-pressurizing but depends on speed, viscosity, geometry, and lubricant supply. At start-up and shutdown, speed may be insufficient to form a full film. Hydrostatic action avoids this limitation by using an external pump. Pressurized lubricant enters recesses or pockets and flows through controlled restrictions into the bearing clearance. The pressure in the pockets supports the load.

The principal dimensionless measure of bearing performance is often the Sommerfeld number,

S = (mu N / p) (R/c)^2,

where mu is dynamic viscosity, N is rotational speed in revolutions per unit time, p is average bearing pressure, R is journal radius, and c is radial clearance. Its precise definition varies among texts. A low Sommerfeld number generally corresponds to high load, low viscosity, low speed, or large clearance and is associated with thin films and greater eccentricity.

Important terms include attitude angle, eccentricity ratio, minimum film thickness, side leakage, oil whirl, oil whip, and cavitation. The eccentricity ratio is epsilon = e/c, where e is the distance between journal and bearing centers. A value approaching unity indicates a very small minimum clearance and a high risk of asperity interaction.

Derivation of the Reynolds Equation

For a Newtonian lubricant, the momentum equation in the direction x of a thin film may be simplified to

0 = -dp/dx + d/dz (mu du/dz),

where p is pressure, u is velocity in the x direction, z is measured across the film, and mu is viscosity. The corresponding transverse pressure gradient is approximately zero:

dp/dz = 0.

These results follow from the thin-film assumptions that film thickness is much smaller than bearing length, pressure is nearly constant across the film, inertial forces are small, and velocity gradients across the film dominate gradients along the bearing.

For constant viscosity, integration across a film bounded by stationary and moving surfaces gives the local volumetric flow rate per unit width:

q = U h/2 - h^3/(12 mu) dp/dx,

where U is the relative surface velocity. The first term is Couette flow produced by surface motion; the second is Poiseuille flow caused by the pressure gradient. Conservation of mass requires

∂h/∂t + ∂q/∂x + ∂q/∂y = 0.

Substitution gives the two-dimensional Reynolds equation:

∂/∂x (h^3/mu ∂p/∂x) + ∂/∂y (h^3/mu ∂p/∂y) = 6U ∂h/∂x + 6V ∂h/∂y + 12 ∂h/∂t,

with consistent sign conventions for surface velocities U and V. For a steady, one-dimensional bearing with constant viscosity and no side-flow, this reduces to

d/dx (h^3 dp/dx) = 6 mu U dh/dx.

The equation is nonlinear because h may depend on position and, in journal bearings, on the unknown attitude and eccentricity. It is also sensitive to boundary conditions. A mathematical solution is not physically meaningful unless the pressure field is limited to the cavitation pressure and the predicted flow is consistent with lubricant conservation.

When viscosity varies with temperature, the equation is written with h^3/mu inside the differential operators. For compressible gases, density must be included, producing a mass-conserving gas-film equation. At high speeds, inertia, turbulence, lubricant additives, and elastic deformation may require extensions beyond the classical Reynolds model.

Boundary Conditions and Cavitation

The commonly used Reynolds boundary conditions for a finite journal or slider bearing are p = ambient pressure at the ends or at specified boundaries, and p = ambient pressure at the outlet. The classical Sommerfeld condition allows pressure to become negative mathematically, which is not physically acceptable for a liquid film. Negative gauge pressure usually indicates cavitation, vapor formation, or air entrainment.

The Swift–Stieber or Reynolds condition sets pressure equal to cavitation pressure at the rupture boundary and imposes zero pressure gradient there. This approach is convenient but does not always conserve mass. The Jakobsson–Floberg–Olsson condition introduces a cavitation zone and ensures mass conservation by accounting for the mixture of liquid and vapor or gas. Modern numerical analyses commonly use Elrod–Adams-type formulations or other mass-conserving algorithms.

Cavitation reduces the pressurized region and changes load, friction, and flow predictions. It may also cause erosion, lubricant oxidation, noise, and fluctuating forces. A designer should therefore distinguish between the full mathematical pressure distribution and the physically admissible pressure field.

Slider and Thrust Bearings

A plane slider bearing consists of a moving runner and a stationary pad separated by a film whose thickness varies along the direction of motion. For a linear wedge,

h(x) = h_1 - (h_1 - h_2)x/L,

where h1 and h2 are inlet and outlet film thicknesses and L is pad length. The Reynolds equation can be integrated analytically for constant viscosity. With the pressure equal to ambient at the inlet and outlet, the pressure distribution is obtained by integrating twice and applying the boundary conditions. The load is

W = b ∫_0^L p(x) dx,

where b is pad width.

For an idealized infinitely wide slider, the pressure is maximum inside the pad rather than at the outlet. The load increases with viscosity and velocity and decreases strongly with increasing film thickness. A smaller outlet-to-inlet thickness ratio can increase pressure generation, but an excessively severe wedge causes high friction, thermal rise, and starvation.

The friction force follows from the wall shear stress:

F = b ∫_0^L [mu U/h + (h/2) dp/dx] dx,

subject to the chosen sign convention. The first term represents direct viscous shear and the second represents the pressure-gradient contribution. The power loss is P = FU. In practical thrust bearings, pads are often pivoted so that each pad develops an appropriate converging wedge despite shaft deflection and thermal distortion. Tilting-pad bearings are therefore more stable and adaptable than fixed-geometry pads, especially in high-speed machinery.

A thrust bearing must also provide adequate cooling and drainage. The heat generated by viscous shear is approximately balanced by conduction into the pad and runner and by convection through the lubricant. The adiabatic or isothermal assumption should be checked rather than accepted automatically.

Journal Bearings

A journal bearing supports a rotating shaft within a cylindrical sleeve. The journal center is displaced from the bearing center under load, producing an approximately converging film in the loaded region. In cylindrical coordinates, the film thickness is commonly written

h(theta) = c[1 + epsilon cos(theta)],

with the angular origin selected according to the chosen convention. The Reynolds equation for a finite journal bearing includes circumferential and axial pressure gradients. In a simplified form,

(1/R^2) ∂/∂theta (h^3 ∂p/∂theta) + ∂/∂z (h^3 ∂p/∂z) = 6 mu omega ∂h/∂theta,

where R is journal radius, z is the axial coordinate, and omega is angular speed.

Two limiting analytical models are widely used. The short-bearing approximation neglects circumferential pressure variation relative to axial pressure variation and is useful when length-to-diameter ratio is small. The long-bearing approximation neglects axial pressure gradients and is more appropriate for large aspect ratios. Real bearings often require numerical finite-difference, finite-element, or finite-volume solutions.

Integrating the pressure field gives radial and tangential load components. Their vector resultant determines load capacity and attitude angle. The minimum film thickness is approximately

h_min = c(1 - epsilon),

under the usual eccentricity convention. As load increases or speed decreases, eccentricity rises and h_min falls. Friction is obtained by integrating shear stress over the journal surface. Side leakage is obtained by integrating the axial flow at the bearing ends. A bearing with high load capacity but excessive leakage or thermal loss may be unsuitable in practice.

Journal-bearing stability is a dynamic issue rather than a static load-capacity issue. Small perturbations in journal position generate changes in fluid-film forces. Linearization produces stiffness and damping coefficients, which enter the rotor equations of motion. Cross-coupled stiffness can destabilize a rotor and produce oil whirl, typically a subsynchronous forward whirl. At higher speeds, oil whip may couple this motion to a rotor natural frequency. Bearing selection must therefore consider the complete rotor-bearing system.

Hydrostatic and Hybrid Bearings

A hydrostatic bearing uses an external pump to deliver lubricant through a restrictor into one or more recesses. The recess pressure supports the load, while the land regions and clearances control flow to the outlet. The pump must supply sufficient pressure even when the shaft is stationary.

A simple hydrostatic pad can be represented by a supply pressure Ps, recess pressure Pr, ambient pressure Pa, and flow resistance Rf. The flow through the restrictor and bearing must be equal. For a laminar restrictor,

Q = (Ps - Pr)/Rr,

while flow through the bearing lands may be approximated by

Q = (Pr - Pa)/Rb(h).

Because land resistance varies strongly with clearance, changes in load alter the film thickness and therefore the recess pressure. This produces hydrostatic stiffness. Constant-flow, constant-pressure, capillary, orifice, and automatic restrictors have different stiffness, flow, and stability characteristics.

Hydrostatic bearing load is approximately the integral of recess pressure over the effective area, with corrections for land pressure and geometry. Pump power is approximately

P_pump = Ps Q / eta,

where eta is pump efficiency. This power is consumed even when the bearing carries a static load. Leakage may be substantial, but the resulting flow can provide excellent cooling and contamination removal.

Hybrid bearings combine hydrodynamic pressure generated by rotation with externally supplied pressure. They offer high stiffness and start-stop protection while reducing pump demand compared with a purely hydrostatic system. Applications include precision machine-tool spindles, coordinate-measuring machines, high-speed turbines, and semiconductor manufacturing equipment.

Thermal Behaviour and Thermohydrodynamic Analysis

The isoviscous Reynolds equation is valuable for preliminary design, but viscosity is strongly temperature-dependent. Shear heating raises lubricant temperature, lowers viscosity, reduces pressure generation, and can further increase film loss. This feedback may create a thermal limit even when an isothermal calculation predicts adequate load capacity.

A thermal analysis combines the Reynolds equation with an energy equation. The energy balance includes viscous dissipation, convection by lubricant flow, conduction into the shaft and bearing, and heat transfer to the surroundings. A practical design may use an iterative procedure:

1. Assume a viscosity and solve for pressure and flow.

2. Calculate shear heating and lubricant temperature rise.

3. Update viscosity using the lubricant temperature–viscosity relation.

4. Repeat until pressure, temperature, and flow converge.

Thermal boundary conditions are often uncertain because housing temperature, shaft heat conduction, oil inlet temperature, and cooling arrangements vary in operation. Thermohydrodynamic analysis becomes especially important for high-speed journal bearings, heavily loaded thrust pads, small clearances, and lubricants with steep viscosity–temperature sensitivity.

Design Assessment and Engineering Trade-offs

Bearing design is a compromise among load capacity, minimum film thickness, friction, temperature, leakage, stability, manufacturability, and reliability. Increasing viscosity generally increases load capacity but also increases friction and heat generation. Reducing clearance can improve hydrodynamic pressure generation but increases sensitivity to thermal expansion, contamination, shaft misalignment, and manufacturing errors. Increasing speed may increase film thickness but can produce unacceptable shear heating or dynamic instability.

A competent assessment normally includes:

• geometry, speed, load, lubricant, and operating-temperature definition;
• pressure and film-thickness prediction;
• friction, flow, power, and temperature estimation;
• cavitation and supply-condition assessment;
• transient start-up and shutdown evaluation;
• rotor dynamic or structural interaction where applicable;
• tolerance, alignment, contamination, and maintenance review.

The bearing material and surface finish must be compatible with the lubricant and operating regime. Soft overlays may tolerate occasional contact, while harder materials may resist wear and deformation. Oil cleanliness, filtration, seal performance, and pump redundancy are often as important as the theoretical pressure distribution.

Applied Case: Hydrostatic Support for a Precision Grinding Spindle

Background

This illustrative case concerns a precision grinding spindle requiring very small radial motion during operation. The spindle must remain supported during start-up, shutdown, and low-speed positioning, while operating at high rotational speed during grinding.

Situation and Problem

A purely hydrodynamic journal bearing was initially considered. Analysis showed that it could support the running load at full speed, but its predicted minimum film thickness during acceleration was small. The machine also required accurate positioning before rotation, making metal-to-metal contact during repeated start-stop cycles unacceptable.

Analysis

The design team compared a hydrostatic bearing with a hybrid bearing. A hydrostatic system offered full load support at zero speed and high radial stiffness, but required a reliable pump, filtration, pressure monitoring, and a reservoir capable of removing heat. A hybrid system could use external pressure during start-up and rely partly on hydrodynamic action during steady operation, reducing flow demand.

The bearing was modelled using the Reynolds equation for the lands and a restrictor-flow equation for each pocket. Load balance was solved simultaneously with the pressure-flow relations. A thermal iteration was then performed using the predicted shear heating and inlet-oil temperature. Dynamic stiffness and damping were estimated by perturbing the shaft position about its equilibrium.

Approach and Solution

The selected design used multiple recessed pockets with capillary restrictors and an auxiliary pressure-monitoring circuit. The restrictors were sized so that pocket pressure remained sufficiently sensitive to clearance changes, providing useful stiffness without excessive pump power. A hybrid operating mode was adopted: high supply pressure during start-up and controlled pressure during normal running.

The design also incorporated fine filtration, a temperature-controlled reservoir, automatic shutdown for low pressure, and leakage collection. Manufacturing controls were placed on radial clearance, pocket depth, restrictor diameter, and shaft roundness.

Outcome

The hybrid arrangement met the start-stop requirement and provided greater stiffness than the original hydrodynamic concept. The case also demonstrated that bearing selection cannot be based solely on steady-state load capacity. Pump reliability, thermal management, contamination control, and dynamic response were decisive design variables.

Learning Points

1. The correct lubrication regime depends on the complete duty cycle, not only the nominal running point.

2. Hydrostatic systems exchange mechanical-contact risk for supply-system complexity.

3. Restrictor selection controls stiffness, flow, and pump power.

4. Thermal and dynamic analyses should be included before finalizing the bearing geometry.

Limitations, Risks, and Common Errors

The classical Reynolds model neglects several effects that may be important in advanced applications. Film thickness may not be small compared with bearing dimensions; inertia may not be negligible; turbulence may occur; lubricant properties may vary with pressure; surfaces may deform elastically; and roughness may influence flow. In such cases, modified Reynolds equations, coupled fluid–structure models, or computational fluid dynamics may be required.

Common analytical errors include using an incorrect sign convention for film slope, applying ambient pressure throughout a cavitated region, ignoring side leakage in a finite bearing, treating viscosity as constant despite a large temperature rise, and comparing results obtained with inconsistent definitions of speed or average pressure. Another frequent mistake is optimizing load capacity while neglecting friction, stability, or pump failure.

Hydrostatic bearings introduce additional hazards. Loss of pump pressure can cause immediate film collapse; blocked restrictors can produce unequal support; contaminated oil can damage precision restrictors; and excessive leakage can overload the reservoir or cooling system. Safeguards should include pressure and temperature monitoring, filtration, alarms, emergency shutdown logic, and, where necessary, redundant pumps.

Digital Analysis and Emerging Practice

Modern bearing design increasingly uses numerical solvers coupled with thermal, structural, and rotor-dynamic models. Finite-difference and finite-element methods solve the Reynolds equation for complex geometry, while computational workflows can perform sensitivity studies over clearance, viscosity, speed, load, and temperature. Reduced-order models are useful for real-time monitoring and control.

Sensors measuring supply pressure, return temperature, shaft displacement, vibration, and flow can support condition-based maintenance. Data-driven models may detect abnormal leakage, rising temperature, or changes in dynamic coefficients. Artificial intelligence can assist anomaly detection, but it does not replace physical validation: a prediction that lacks mass conservation, thermal consistency, or explainable failure criteria is unsuitable for safety-critical bearing decisions.

Current research includes textured surfaces, low-viscosity and biodegradable lubricants, porous and compliant bearings, active restrictors, additive-manufactured supply networks, and digitally controlled hybrid bearings. These developments aim to improve efficiency and adaptability, but they also increase the importance of model verification, material compatibility, contamination control, and lifecycle assessment.

Best-Practice Design Guidance

Use the simplest model that captures the dominant physics, then verify it with a higher-fidelity model or experiment when the design margin is small. State every assumption and boundary condition. Use mass-conserving cavitation treatment where flow prediction matters. Couple pressure calculations with thermal analysis for high-speed or heavily loaded bearings. Evaluate start-up, shutdown, transient overload, and loss-of-supply conditions. Finally, specify tolerances, filtration, monitoring, and maintenance requirements together with the bearing geometry.

Chapter Summary

Hydrodynamic lubrication generates pressure through relative motion and a converging film, whereas hydrostatic lubrication uses an external pump to support load independently of speed. The Reynolds equation is obtained from thin-film momentum and continuity equations and provides the foundation for analysing pressure, load, flow, and friction. Journal, slider, and thrust bearings require different geometrical representations and boundary conditions. Cavitation must be treated physically, preferably with mass-conserving methods when flow prediction is important.

Hydrostatic bearing performance depends on restrictor characteristics, pocket pressure, leakage, stiffness, and pump power. Hybrid bearings combine externally supplied pressure with self-generated hydrodynamic action. In practical design, thermal effects, stability, side leakage, manufacturing tolerances, contamination, and supply reliability are as important as nominal load capacity. Numerical and sensor-based tools improve analysis and monitoring, but they must remain consistent with fluid mechanics and conservation principles.

Key Terms

Hydrodynamic lubrication: Fluid-film lubrication in which relative motion generates the supporting pressure.

Hydrostatic lubrication: Lubrication in which an external pump supplies pressure to support load.

Hybrid lubrication: Lubrication combining hydrodynamic and hydrostatic pressure generation.

Reynolds equation: Thin-film fluid-flow equation derived from momentum and continuity relations.

Film thickness: Local separation between the bearing surfaces.

Minimum film thickness: Smallest lubricant-film separation in the bearing.

Eccentricity ratio: Journal eccentricity divided by radial clearance.

Attitude angle: Direction of journal-center displacement relative to the applied load.

Sommerfeld number: Dimensionless parameter relating viscosity, speed, load, radius, and clearance.

Couette flow: Flow caused by motion of a bounding surface.

Poiseuille flow: Pressure-gradient-driven flow through the lubricant film.

Cavitation: Formation of a vapor or gas-filled region where liquid pressure reaches a limiting value.

Side leakage: Lubricant flow escaping through the axial sides of a bearing.

Restrictor: Device controlling lubricant flow into a hydrostatic bearing pocket.

Bearing stiffness: Change in supporting force per unit change in displacement.

Cross-coupled stiffness: Fluid-film force coefficient coupling motion in one direction to force in another.

Oil whirl: Subsynchronous fluid-induced rotational motion of a journal.

Thermohydrodynamic analysis: Coupled solution of fluid-film and thermal equations.

Starvation: Condition in which lubricant supply is insufficient to fill the inlet region.

Mass-conserving cavitation: Cavitation formulation that preserves liquid and mixture mass balances.

Review Questions

Short Answer Questions

1. Why is a converging film required for hydrodynamic pressure generation?

2. State the principal assumptions used in deriving the classical Reynolds equation.

3. Distinguish Couette flow from Poiseuille flow in a bearing film.

4. What is the physical meaning of the eccentricity ratio in a journal bearing?

5. Why does a hydrostatic bearing require a restrictor?

Long Answer Questions

1. Derive the two-dimensional Reynolds equation from the thin-film momentum and continuity equations.

2. Explain the pressure generation, load capacity, friction, and leakage characteristics of a slider bearing.

3. Discuss the analysis of a finite journal bearing, including eccentricity, attitude angle, side leakage, and minimum film thickness.

4. Compare hydrodynamic, hydrostatic, and hybrid bearings in terms of load support, start-stop behaviour, stiffness, energy consumption, and reliability.

5. Explain why thermal effects and dynamic stability must be considered in high-speed bearing design.

Analytical / Application Questions

1. A journal bearing experiences increased load while speed and lubricant viscosity remain constant. Predict the qualitative changes in eccentricity ratio, minimum film thickness, friction, and stability margin, and justify each prediction.

2. Design a preliminary investigation for a hydrostatic thrust bearing whose pump pressure is fixed but whose pad clearance varies during operation. Identify the governing equations, boundary conditions, measurements, and failure risks.

3. A numerical bearing solution predicts substantial negative pressure over part of the film. Diagnose the likely modelling problem and propose a physically appropriate cavitation treatment.

22. Multiple Choice Questions with Answers

Question 1

Which mechanism directly generates pressure in a conventional hydrodynamic bearing?

A. External pump pressure only

B. Relative motion through a converging lubricant film

C. Thermal expansion of the bearing housing

D. Surface roughness acting without lubricant flow

Correct Answer: B. Relative motion through a converging lubricant film

Question 2

In the Reynolds equation, the term involving h cubed primarily reflects the effect of:

A. Film-thickness control of pressure-driven flow

B. Bearing-material hardness

C. Lubricant density alone

D. Shaft rotational inertia

Correct Answer: A. Film-thickness control of pressure-driven flow

Question 3

Why is negative pressure from the classical Sommerfeld solution physically problematic for a liquid lubricant?

A. It implies infinite viscosity

B. It generally indicates a cavitated region rather than a sustained liquid pressure

C. It proves that the bearing is hydrostatic

D. It means that the film is completely rigid

Correct Answer: B. It generally indicates a cavitated region rather than a sustained liquid pressure

Question 4

For a journal bearing with radial clearance c and eccentricity e, the eccentricity ratio is:

A. c/e

B. e+c

C. e/c

D. e-c

Correct Answer: C. e/c

Question 5

Which flow component is caused directly by the motion of a bounding surface?

A. Couette flow

B. Poiseuille flow

C. Cavitational flow

D. Restrictor flow

Correct Answer: A. Couette flow

Question 6

A hydrostatic bearing can support a static load because:

A. Rotation always produces a converging wedge

B. An external pump supplies pressurized lubricant

C. The lubricant has zero viscosity

D. The bearing operates without leakage

Correct Answer: B. An external pump supplies pressurized lubricant

Question 7

If lubricant temperature rises substantially in a high-speed bearing, the usual consequence is that viscosity:

A. Increases indefinitely

B. Remains exactly constant

C. Decreases, potentially reducing pressure generation

D. Becomes independent of film thickness

Correct Answer: C. Decreases, potentially reducing pressure generation

Question 8

What is a principal function of a restrictor in a hydrostatic bearing?

A. To control flow and establish pocket pressure

B. To eliminate all heat generation

C. To increase shaft eccentricity deliberately

D. To prevent any lubricant from leaving the bearing

Correct Answer: A. To control flow and establish pocket pressure

Question 9

Oil whirl is most appropriately described as:

A. A static deformation of the bearing pad

B. A subsynchronous fluid-induced motion of the journal

C. A form of hydrostatic leakage

D. A thermal cracking mechanism

Correct Answer: B. A subsynchronous fluid-induced motion of the journal

Question 10

Which design change commonly increases hydrodynamic load capacity but may also increase friction and thermal loss?

A. Reducing lubricant viscosity

B. Increasing lubricant viscosity

C. Removing the converging wedge

D. Eliminating all pressure gradients

Correct Answer: B. Increasing lubricant viscosity