Fluid Bearings Notes

Aerostatic vs Hydrostatic Bearings

• Fluid media classifications:

  • Aerostatic (air) bearings use compressible fluids such as compressed air or nitrogen.

  • Hydrostatic bearings use incompressible liquids such as oil or water.

• Load capacity considerations:

  • Aerostatic/air bearings have a load capacity limited by the available air pressure; example given: 100 psi shop air.

  • Air bearings are suitable for high-speed motion.

  • They do not require seals in clean-room-like environments.

• Stability and damping:

  • Due to low viscosity, air bearings can be unstable if not properly designed and have minimal to moderate damping characteristics.

• Hydrostatic bearings advantages:

  • Can be supplied with fluid under high pressure, providing very high load capacity in a limited space.

  • When using liquid (oil) or viscous fluids, hydrostatic bearings can exhibit high damping.

  • Best suited for applications with low to moderate velocity of motion.

• Hydrostatic bearing drawback:

  • The recirculated fluid must be reclaimed and recirculated.

  • Recirculated fluid can be temperature-controlled, helping to manage machine temperature.

• Fluid bearing materials:

  • Can be made from a wide range of materials; common examples include:

  • DuraBar, a cast iron-like material with low thermal expansion;

  • cast iron, bronze, aluminum, stainless steel, iron, graphite, epoxies, and various plastics.

• Manufacturing and surface finishing:

  • Bearing surfaces are manufactured to tight tolerances and roughness via processes such as grinding, lapping, and diamond turning.

• Fundamental relation for lifting force:

  • The weight or lifting force supported by a fluid thrust bearing is given by

  • $W = P<em>R A</em>E$

  • where:

  • $P_R$ = recessed pressure,

  • $A_E$ = effective area of the bearing.

• Recessed pressure and flow relationship:

  • The recessed pressure depends on the flow through the restrictor and the flow across the bearing land.

  • Restrictors are used to control flow rate and recessed pressure, and they produce low changes, thereby creating stiffness.

  • Restrictors are usually designed to restrict supply pressure by about 50%.

  • Flow rate $q$ is a function of recessed pressure, bearing height $h$, dynamic viscosity $<br>ho$ (mu), and a flow shape factor $\beta$; the shape factor is based on the bearing shape:

  • $q = f(P_R, h, \beta, <br>ho)$

• Bearing height and manufacturing:

  • Bearing height is often limited by manufacturing capability and is chosen with the bearing shape to minimize flow for a given load range.

• Power considerations:

  • Larger flow results in more power required to pump the fluid.

  • Fluid bearings exhibit zero static friction, but experience dynamic friction when in motion.

  • Dynamic friction $f$ is affected by bearing height, fluid viscosity, bearing land surface area, and speed $u$:

  • $P_{ ext{friction}} = f u$

• Friction management:

  • Because fluid bearings exhibit friction, the frictional area should be limited to the bearing land.

  • Common practice is to set recessed depth (pocket) to be at least 16 to 20 times the bearing height or film thickness:

  • $ext{Depth} \ge 16h ext{ to } 20h$

• Thermal effects and overall power:

  • Pumping power and frictional power together constitute the total power, which correlates with temperature rise in the bearing:

  • $P<em>{ ext{total}} = P</em>{ ext{pump}} + P_{ ext{friction}}$

  • $P<em>{ ext{pump}} = P</em>{ ext{sup}} imes q$

  • $P_{ ext{friction}} = f imes u$

• Heat generation and temperature rise:

  • Friction and pumping generate heat; as pressurized fluid is released to atmosphere, shearing occurs and contributes to heat generation equal to the pump power.

  • The change in temperature due to generated heat is given by

  • $\Delta T = \frac{P_{ ext{total}}}{q \rho c}$

  • where:

  • $\rho$ = fluid density,

  • $c$ = specific heat capacity of the fluid.

  • Note: $J$ is the mechanical equivalent of heat; in SI units, it is generally unnecessary to insert a numerical value for $J$ since mechanical energy and heat energy are expressed consistently in SI units.

• Damping characteristics in hydrostatic oil bearings:

  • Due to squeeze-film damping, oil hydrostatic bearings are considered vibration- and shock-resistant.

  • Damping is most effective in the direction normal to motion and is low in the direction of motion.

  • Achieving good shear damping requires balancing bearing gap, bearing area, and bearing stiffness.

• Bearing pad geometries:

  • The most common bearing pad geometries are:

  • circular pads,

  • angular pads,

  • rectangular pads,

  • journal bearings.

• Circular thrust bearings:

  • Used around bearings in linear slides, planar slides, and as support bearings (e.g., supporting a rotating disc).

  • For circular thrust bearings, the effective area $A<em>E$ and flow rate $q$ depend on the outer radius $r</em>o$ of the bearing pad and the inner radius $r_i$ of the recess pocket; the exact equations are defined in the standard equations (not shown in the transcript).

• Angular thrust bearings:

  • Commonly used as the thrust bearing for rotating shafts; also used in oil hydrostatic spins.

  • The effective area and flow rate for angular thrust bearings are defined by corresponding equations (not shown in the transcript).

• Rectangular thrust bearings:

  • Rectangular thrust bearings with ReadyI machined into the corners of the recess are the most commonly used pattern for hydrostatic linear positioning systems.

  • The ReadyI features are added for ease of machining and are usually equal to the radius of the end mill used to machine the bearing recess.

• Readyi features and “ReadyEye” terminology:

  • The transcript mentions Readyi (and ReadyEye) for the annular recess in inner and outer lenses, with ReadyI four positions.

  • Rectangular thrust bearings with Readyi machined into the corners of the recess are common for hydrostatic linear positioning systems; corner Readyi ease machining and typically match the end mill radius used for machining.

• Parameters for rectangular and annular recess bearings:

  • For rectangular patterns, the effective bearing area, dimensionless flow factor, and flow rate are given by equations involving the recess width $a$, recess length $b$, bearing land width $c$, and corner fillet radius $r$:

  • variables:

  • $a$ = width of the recess,

  • $b$ = length of the recess,

  • $c$ = width of the bearing land,

  • $r$ = radius of the corner fillet.

  • The transcript notes that the equations define the effective bearing area, dimensionless flow factor, and flow rate, but the explicit formulas are not provided.

• Post pad bearing designs:

  • The transcript begins to mention "Post pad bearing designs are another common" but the statement is cut off, leaving this point incomplete.

• Connections and context:

  • Fluid bearings connect to fundamental tribology concepts: low static friction, controlled damping, and the interplay between film thickness, load, and flow.

  • The choice between air, hydrostatic oil, or other fluids ties to application requirements: speed, stiffness, damping, heat generation, and maintenance (recirculation).

• Practical design implications:

  • Achieving adequate stiffness and damping requires careful control of gap height, land area, and stiffness of the bearing structure.

  • Temperature management is integral due to pumping and frictional heating; recirculation and temperature control of the circulated fluid are important.

  • Material selection impacts thermal expansion, stiffness, and machinability; common options include metals and advanced composites.

• Ethical/philosophical/practical implications:

  • Design trade-offs involve energy efficiency (pumping power), reliability (damping and vibration resistance), and manufacturing feasibility.

  • Recirculation and energy use have pragmatic implications for system efficiency and environmental concerns in industrial settings.

• Summary takeaway:

  • Fluid bearings leverage controlled pressure, precise geometry, and recirculation to achieve high stiffness and damping with low static friction, but require careful design to manage frictional losses, heat generation, and manufacturability.