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

<details>
<summary>

### Plain Journal Bearings

</summary>

- 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

</details>

<details>
<summary>

### Ball and Roller Bearings (Rolling Element Bearings)

</summary>

- 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

![](./images/bearings_1-010.jpg)

![](./images/bearings_1-011.jpg)

</details>

<details>
<summary>

### Plain Rubbing Bearings (Dry Sliding)

</summary>

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

</details>

<details>
<summary>

### Oil Lubricated Porous Bearings

</summary>

- 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

</details>

<details>
<summary>

### Hydrodynamic Bearings

</summary>

- 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



![](./images/vimscrot-2022-11-15T17:56:26,739425867+00:00.png)

</details>


# fun graphs that may be useful for bearing selection

![](./images/bearings_1-035.jpg)

![](./images/vimscrot-2022-11-15T17:33:30,763609479+00:00.png)

![](./images/vimscrot-2022-11-15T17:51:56,506933942+00:00.png)

# $pV$ 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 $0.5pV_\text{max}$

![$P_\text{max}$ is limited by strength, $V_\text{max}$ is limited by temperature rise](./images/bearings_1-036.svg)

- 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

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

$$V = \omega\frac D2$$

![](./images/vimscrot-2023-04-28T18:17:05,184873693+01:00.png)


## Axial Sliding Bearing

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

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

![](./images/vimscrot-2023-04-28T18:17:16,580658677+01:00.png)

## 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)