notes/uni/mmme/2044_design_manufacture_and_project/bearings.md

author	date	title	tags	uuid	lecture_slides	anki_deck_tags
Akbar Rahman	\today	MMME2044 // Bearings	bearings	94cac3fd-c352-4fdd-833d-6129cb484b8a	./lecture_slides/Lecture 7 - Bearings 1 – Plain Hydrodynamic Bearings 1.pdf ./lecture_slides/Lecture 11 - Bearings 2 - Rolling Element Bearings.pdf	bearings

I don't think I ever finished these notes.

Errata

Lecture Slides 2 (Lecture 11), slide 18

Static load carrying capacity equation is

S_0 = \frac{P_0}{C_0}

but should be:

S_0 = \frac{C_0}{P_0}

If the load applied to a bearing is half of its rated capacity, then you have a safety factor of 2. Therefore the equation in the slides must be incorrect.

Types of Bearings

Plain Journal Bearings

• used to support rotating shafts loaded in radial directions
• consists of an insert fitted between the shaft and support
• the insert may be an aluminium alloy, copper alloy, or other material
• the insert provides lower friction and less wear than if just rotating in the support
• the bearing may be dry rubbing or lubricated

Lubrication

• hydrodynamic---a shaft continuously in oil. the load is carried by pressure generated in the oil as a result of the rotation
• hydrostatic---avoids excessive wear at start up by pumping oil into the load bearing area at a pressure that lifts the shaft
• solid-firm---a coating of a solid material like graphite or molybdenum disulphide
• boundary layer---a thin layer of lubricant which adheres to the surface of the bearing

Ball and Roller Bearings (Rolling Element Bearings)

• main load is transferred from rotating shaft to its support by rolling contact from balls
• a rolling element bearing consists of an inner race, outer race, rolling elements and a cage

Plain Rubbing Bearings (Dry Sliding)

• does not use liquid lubrication
• usually polymeric
• dry lubricants added (e.g. PTFE)
• reinforcements added (e.g. glass fibre)

Oil Lubricated Porous Bearings

• manufactured from sintered metal powders
• porous and oil impregnated
• more porous is weaker but allows for high speeds
• lubricant needs to replenished at regular intervals --- usually every 1000 hours of use

Hydrodynamic Bearings

• pressure builds up in the lubricant as a response to the relative motion
• both journal and thrust bearings may use this principle
• surfaces touch and rub at very low speeds

fun graphs that may be useful for bearing selection

pV Factor

• a measure of the bearing's ability to cope with frictional heat generation
• rapid wear occurs at pV_\text{max}
• if the value is exceeded then overheating, melting, and excessive wear or seizure may follow
• general operational range should be around 0.5pV_\text{max}

• A - thermoplastics
• B - PTFE
• C - PTFE + fillers
• D - porous bronze + PTF + lead
• E - PTFE-glass weave + thermoset
• F - reinforced thermoset + molybdenum disulphide
• G - thermoset/carbon graphite + PTFE

Radial Sliding Bearing

p = \frac{F_\text{radial}}{bD}

V = \omega\frac D2

Axial Sliding Bearing

p = \frac{4F_\text{axial}}{\pi(D^2-d^2)}

V = \omega\frac{D+d}{4}

Plain Rubbing Bearings

• does not rely on liquid lubricaton
• usually made of polymers and moulded to final shape
• dry lubricants like ptfe are added
• reinforcements like glass fibres can be added
• pressure is limited by strength
• speed is limited by temperature

Oil Lubricated Porous Bearings

• manufactured from sintered metal powders
• porous & oil impregnated
• more porous bearings are weaker but can run at higher speeds
• lubricant needs to be replenished at regular intervals

Wear

K = \frac{W}{FVt}

where K is wear factor (provided by manufacturer), W is wear volume, F is sliding velocity, F is bearing load, and t is elapsed time.

Manufacture

• nominal diametral clearance is commonly 1 $\mu$m per mm

• manufacturing tolerance

  • close running fit (H8/f7)
  • free running (H9/d9)