mmme2044 add incomplete notes on pneumatics, bearings

uni/mmme/2044_design_manufacture_and_project/bearings.md

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+---
+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 ]
+---
+
+> I don't think I ever finished these notes.
+
+# 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)
+
+
+
+# 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-2022-11-15T17:48:21,486895199+00:00.png)
+
+
+## Axial Sliding Bearing
+
+$$p = \frac{4F_\text{axial}}{\pi(D^2-d^2)}$$
+
+$$V = \omega\frac{D+d}{4}$$
+
+![](./images/vimscrot-2022-11-15T17:48:34,860294942+00:00.png)
+
+# 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)
+