# Hydrodynamic plain bearing

Oil pressure and forces in a hydrodynamic radial plain bearing
Diameter difference between bushing and shaft exaggerated, in reality only about 3 ‰

The hydrodynamic plain bearing is a plain bearing in which the lubricant pressure automatically builds up when the bearing is in operation at the point where the force is transmitted between the two bearing parts. The lubrication gap is wedge-shaped at this point (lubrication wedge), so that higher pressure arises in the lubricant carried by the surface of the moving bearing part into the constriction, or the power is transmitted via an interposed lubricant film.

With hydrostatic plain bearings , lubricant is supplied to the power-transmitting point by an external pump and under the required pressure. Since the pump can work permanently, there is also lubricant friction at the beginning and at the end of bearing operation (during start-up and coasting down). However, the pressure that is required for highly loaded bearings and that occurs in hydrodynamic plain bearings would not be easy to produce with a pump. Highly loaded hydrodynamic plain bearings are occasionally also equipped with a pump for starting and coasting.

Stribeck curve (schematic):
coefficient of friction μ as a function of the relative speed in the lubrication gap of a hydrodynamic plain bearing
Lemon Game Storage with Pressure Distribution; The difference in radius between the shells and the shaft is exaggerated

## function

Explanation using the example of the vertically loaded hydrodynamic, oil-operated radial bearing .

### The lubricating wedge

One of the two sides of the bottleneck that occurs in the bearing bush when the shaft is in an eccentric position acts as a lubricating wedge (see figure above: bottleneck marked in red). The rotating shaft transports ("pumps") oil adhering to its surface into the wedge. As a result of the narrowing of the cross-section, the oil pressure increases there. The position and thickness of the gap are the result of an automatic process. The shaft is also slightly eccentric horizontally in the bushing so that the resulting oil pressure force in the wedge gap is directed against the force of gravity of the shaft. ${\ displaystyle P}$${\ displaystyle F}$

### Friction and speed

In hydrodynamic plain bearings, the coefficient of friction is a function of the speed (more precisely: the relative speed between the sliding surfaces), which is represented with the help of the Stribeck curve (see figure). There are speed ranges with different types of friction:

1. Standstill / solid body friction
2. low speed / mixed friction
3. high speed / fluid friction

When starting up, the static friction is overcome and the shaft initially rotates with sliding friction . The sliding friction is initially mixed friction, which decreases until the speed is high enough for fluid friction. When the speed is increased, the coefficient of friction increases again (increased flow resistance in the lubricating film). If the speed is too high, the eccentric position of the shaft in the radial bearing becomes too small for a clear lubrication gap geometry. A gap occurs briefly one after the other at any point on the circumference, which leads to vibrations in the bearing and to its destruction. High-speed radial bearings can be stabilized by making a socket with two ("lemon game bearings", see illustration) or more curved wedge surfaces instead of a round socket.

For safety reasons, the nominal speed is selected above the reversal point in the Stribeck curve.

The theory about friction in currents comes mainly from Osborne Reynolds . Arnold Sommerfeld applied them to the processes in hydrodynamic plain bearings. The Sommerfeld number comes from him , a dimensionless number consisting of several physical quantities. In particular, this characterizes the relationship between speed and bearing load and is used to classify the various areas of application of the hydrodynamic plain bearing. ${\ displaystyle So}$

The summer field number is defined as follows:

${\ displaystyle So = {\ frac {p_ {m} \ cdot \ Psi ^ {2}} {\ eta \ cdot \ omega}}}$
• ${\ displaystyle p_ {m} \;}$: bearing load related to the projected storage area (diameter times width) ${\ displaystyle F = P}$
• ${\ displaystyle \ Psi \;}$: relative bearing clearance (diameter difference / nominal diameter)
• ${\ displaystyle \ eta \;}$: dynamic viscosity of the lubricant at the temperature in the lubrication gap
• ${\ displaystyle \ omega \;}$: Angular velocity of the shaft
Gümbel curve (schematic):
position of the wave center as a function of the Sommerfeld number So
(quarter of the small circle in the middle of the first illustration, enlarged)

It serves, for example, as a parameter in the Gümbel curve (see figure; named after Ludwig Gümbel ), with which the relative position of the shaft center to the center of the socket is shown.

The following Sommerfeld numbers and areas of application belong together:

Summer field number scope of application
So <1 Fast run area
1 < So <3 Medium load range
So > 3 Heavy duty area
1 < So <10 best usable Sommerfeld numbers
10 < So ≤ ∞ no application: mixed friction
So = ∞ no application: standstill

## Slide bearings in comparison with roller bearings and in comparison of their types

### Slide bearing advantages over roller bearings

As a result of economically favorable mass production by specialized manufacturing companies and standardization of their properties, rolling bearings are a "more manageable" machine element than plain bearings. However, you cannot generally replace the latter because of their several important advantages.

• low noise
• insensitive to shock
• low construction volume
• highest speeds possible
• high guidance accuracy (hydrodynamic multi-surface and hydrostatic bearings)
• easy assembly by dividing the socket
• long service life in continuous operation (with hydrostatic lubrication theoretically no wear)

• Plain bearings require a permanent oil supply, which often requires additional lines, bores and a pump.
• Due to the necessary oil flow, they are not suitable for applications that have to use oil sparingly (e.g. two-stroke engines because of the mixture lubrication ).
• Limited suitability for operation in the mixed friction range (Sommerfeld number> 10), i.e. in the combination of low speeds, frequent start-up processes with high loads
• Limited emergency running properties

### Comparison of hydrodynamic and hydrostatic plain bearings

Hydrostatic plain bearings have a lower power requirement (pump power plus bearing friction) than hydrodynamic bearings because they work as pumps with poor efficiency . This changes at high peripheral speeds, at which the flow in the chambers of the hydrostatic bearings becomes turbulent, so that the more favorable pumping efficiency is no longer decisive for the power requirement.

For safety reasons, hydrodynamic bearings are preferred even when the rotational speed is not very high, because an oil supply of 50 to 1000 bar represents a risk. This is z. B. not included in turbines despite possible power savings. An additional oil pump (<50 bar) is only switched on when the turbines rarely stop and restart.

Hydrostatic plain bearings are preferred where shafts (e.g. machine tool spindles) have to run as centrically as possible. But about 90% of all plain bearings run hydrodynamically.

### Selected applications

The hydrodynamic plain bearing is mainly used in large and heavy machine construction, where heavy shafts with large diameters (high circumferential speeds) have to be stored. A typical example is the bearing of the long shafts of a turbine generator machine group in electric power plants. This is not stopped for months, which is why the start-up and shutdown times (possible wear, but mostly hydrostatically supported) are negligible.

In internal combustion engines , the crankshaft bearings act i. d. R. hydrodynamic. When the engine is started, the pressure of the oil pump is also added. In the case of large engines (e.g. marine engines), the oil pump system is started in advance so that the lubrication is already improved at start-up. When the motor vehicle engines start up, there is initially only mixed friction. Your bearings have to get by with the oil still adhering from previous use.

Hydrodynamic plain bearings are also advantageous for extremely fast rotating runners, e.g. B. can be used in turbo machines and turbochargers . In the spindle motor of hard disk drives, they are used both as hydrodynamic and aerodynamic slide bearings ( air bearings , “lubricant” is air). With the aerodynamic slide bearing, the read heads float on an air cushion above the hard drives.

## Individual evidence

1. The micro-roughness on the surfaces of the shaft and bearing shell store the lubricant. Tests have shown that surfaces that are too smooth or even polished reduce the load-bearing capacity and service life of the bearing. The special features of these friction conditions are examined and described by tribology .
2. A small remaining distance is required so that there is a force couple as a reaction torque against the torque loss due to friction in the oil.
3. ^ Hans Herbert Ott: Machine Design , Volume IIIb, Lectures at the ETH Zurich , AMIV-Verlag Zurich, 1978.