Hydrostatic and Hydrodynamic Bearings

In this tutorial, you will learn about the two most common types of sliding contact bearings and understand the design considerations associated with each. In short, you will study the working principle of these bearings and learn the characteristics associated with each.

Contents:

1. What is Hydrostatic Bearings?
2. Energy Losses in Hydrostatic Bearings
3. What are Hydrodynamic Bearings?
4. Reynolds Equation for Bearings
5. Design of Bearings
6. Construction of Bearings
7. Materials used in Bearings
8. Sintered Metal Bearings

What is Hydrostatic Bearings?

The hydrostatic bearings are those bearings that can support steady loads without any relative motion between the journal and the bearing itself. They achieve this by forcing externally pressurized lubricants between the members. The following figure shows a Hydrostatic Step Bearing.

Here,
W = thrust load (N)
R_o = outer radius of the shaft (mm)
R_i = radius of the recess or the pocket (mm)
P_i = supply of inlet pressure (N/mm²) or (MPa)
P_o = outlet or atmospheric pressure (N/mm²) or (MPa)
h_o = fluid film thickness (mm)
Q = flow of the lubricant (mm³/s)
m = viscosity of the lubricant (N-s/mm²) or (MPa-s)

• Hydrostatic bearing demonstrates high stiffness and long bearing life. They can accommodate heavy loads at low speeds.
• The design of this bearing is very complex and requires precision pressure and gap control to operate properly without damage.
• hydrostatic bearings cannot be used in applications where the speed of the journal is greater than 2 m/s because the viscous shear of the fluid in the bearing gap generates too much heat.
• Since these bearings are essentially noncontact devices, they have an infinite life.

Energy Losses in Hydrostatic Bearings

The total energy loss in a hydrostatic and a hydrodynamic bearing consists of two factors, the energy required to pump the lubricating oil and energy loss due to viscous friction. The following figure shows the pressure distribution in the bearing. The following figure shows the pressure distribution in a Hydrostatic bearing.

• The power required to pump the oil is given by
  E_P = Q (Pi_i-P_o) N-mm/s
  E_P = Q (Pi_i-P_o)(10^-6) kW
  Where E_P is the power loss due to Pumping.
• The frictional power loss is determined by considering the elemental ring of radius (r) and radial thickness (dr). The viscous resistance for this ring is (dF). It is determined by Newton’s law of viscosity. It is represented by E_F.
• The total energy loss is given by the following equation
  E_T = E_P + E_F

What are Hydrodynamic Bearings?

The gap in hydrodynamic bearings is produced dynamically by the bearing motion. In rotary applications, hydrodynamic bearings may require additional pressure on one of the bearing pads or a secondary bearing to minimize excessive friction while commencing rotation.

• Hydrodynamic bearings must be created to accommodate either radial or thrust loads, or both.
• A hydrodynamic bearing is a low-clearance assembly that relies on a film of oil, and occasionally air, that develops as the spindle rotates.
• It features a cylindrical bore with two axial lubricating grooves. This bearing has a high load capacity and a basic design that is small, bi-rotational, and simple to produce.
• Circumferential groove bearings, pressure bearings, and multiple groove bearings are the three fundamental types of hydrodynamic bearings. Hydrodynamic bearings are commonly used for fine machining and finishing because of their high stiffness and extended bearing life.

Reynolds Equation for Bearings

The theory of hydrodynamic lubrication is based on a differential equation derived by Osborne Reynold. This equation is given below.

\(\frac{∂}{∂x} [h^3 \frac{∂p}{∂x}]+\frac{∂}{∂z} [h^3 \frac{∂p}{∂z}]=6μU \frac{∂h}{∂x}\)
In the equation, h is the fluid film thickness, μ is the viscosity index and U is the fluid velocity associated with the film thickness.
The Reynolds equation is based on some assumptions listed below.

• The lubricant obeys Newton’s law of viscosity.
• The lubricant is incompressible.
• The inertia forces in the oil film are negligible.
• The viscosity of the lubricant is constant.
• The effect of the curvature of the film concerning film thickness is neglected. It is assumed that the film is so thin that the pressure is constant across the film thickness.
• The shaft and the bearing are rigid.
• There is a continuous supply of lubricant.

Design of Bearings

Bearing design involves the selection of multiple criteria which affect the performance and characteristics of the sliding contact bearing. Some of these parameters are discussed here.

• The length to diameter ratio (l/d) affects the performance of the bearing. As the ratio increases, the resulting film pressure increases. A long bearing, therefore, has more load-carrying capacity compared with a short bearing. A short bearing, on the other hand, has greater side flow, which improves heat dissipation.
• The unit bearing pressure is the load per unit of the projected area of the bearing in running condition. It depends upon several factors, such as bearing material, operating temperature, the nature and frequency of load, and service conditions.
• The start-up load is the static load when the shaft is stationary. It mainly consists of the dead weight of the shaft and its attachments. The start-up load can be used to determine the minimum length of the bearing based on starting conditions.
• The radial clearance should be small to provide the necessary velocity gradient. However, this requires costly finishing operations, rigid mountings of the bearing assembly, and clean lubricating oil without any foreign particles. This increases the initial and maintenance costs.
• The surface finish of the journal and the bearing is governed by the value of the minimum oil film thickness selected by the designer and vice versa.
• The lubricating oil tends to oxidize when the operating temperature exceeds 120°C. Therefore, the operating temperature should be kept within these limits. In general, the limiting temperature is 90°C for bearings made of babbitts.

Construction of Bearings

A typical bearing consists of the shaft or the journal, the sleeve, and the lubricant. Manufacturing and design considerations have influenced the design of these components to maximize efficiency.

• There are two types of bearing construction— solid bushing and lined bushing. A solid bushing is made either by casting or by machining from a bar. A lined bushing consists of a steel backing with a thin lining of bearing material like babbitt. It is usually split into two halves.
• There are two basic types of patterns of oil grooves— circumferential and cylindrical.
• A circumferential oil-groove bearing divides the bearing into two short bearings. The pressure developed in the bearing along the axis is reduced due to the groove. This results in a lower load-carrying capacity. Circumferential oil-groove bearings are used for the connecting rods and crankshafts of automotive engines.
• The cylindrical oil groove bearing has an axial groove almost along the full length of the bearing. It has a higher load carrying capacity compared with the circumferential oil-groove bearing. Cylindrical oil-groove bearings are used for gearboxes and high-speed applications.
• An oil ring bearing consists of a bearing with an oil ring dipping into the oil bath below. The diameter of the oil ring is large compared with the diameter of the shaft. As the shaft rotates, the oil ring also rotates, although at a considerably lower speed, and carries along with it the oil from the oil bath to the shaft. There are spreader grooves, which carry the oil to the entire surface of the shaft. The use of the oil ring bearing is restricted to horizontal shafts.

Materials used in Bearings

Bearings are precision machine elements that must be made from materials suitable for completing their goal. Below, we see a few of the most desirable characteristics for a bearing material and the reasoning behind it.

• When metal to metal contact occurs, the bearing material should not damage the surface of the journal. It should not stick or weld to the journal surface.
• It should have high compressive strength to withstand high pressures without distortion.
• The bearing material should have sufficient endurance strength to avoid failure due to pitting in cases of fluctuating stresses.
• The bearing material should have the ability to yield and adapt its shape to that of the journal. This property is called conformability. When the load is applied, the journal is deflected resulting in contact at the edges. A conformable material adjusts its shape under these circumstances.
• The bearing material should be soft to allow particles to get embedded in the lining to avoid further trouble caused due to contamination. This property of the bearing material is called embeddability.
• In applications like engine bearings, the excessive temperature may cause the oxidation of lubricating oils and forms corrosive acids. Thus, bearing material should have sufficient corrosion resistance.
• The most popular bearing material is babbitt. Due to its silvery appearance, babbitt is called white metal. The other bearing materials are bronze, copper–lead, aluminum alloys, and plastics.

Sintered Metal Bearings

Sintered metal powder bearings are made from compressed metal powder by the sintering process. They are porous bearings impregnated with lubricating oils. They can absorb lubricating oil to the extent of 20% to 30% of their volume.

• This oil serves as a reservoir enabling the bearing to run for a long period without any attention. They can be refilled with oil by soaked felts or wick-feed lubricators at periodic intervals without dismantling.
• There are two grades of sintered bearings, copper-base, and iron-base. A copper-base material has more corrosion resistance compared with an iron-base material.
• The permissible bearing pressures for copper-base and iron-base bearings are 60 N/mm² and 100 N/mm² respectively. They are capable of giving a satisfactory performance up to 80°C.
• Sintered metal powder bearings are used in automobiles, textile machinery, and machine tools.