78 lines
3.1 KiB
Markdown
78 lines
3.1 KiB
Markdown
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---
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author: Akbar Rahman
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date: \today
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title: MMME2046 // Vibrations // Isolation
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tags: [ vibration, vibration_isolation ]
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uuid: fcdf1af0-9d54-4a6b-82fe-ef2c9f30ecb7
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lecture_slides: [ ./lecture_slides/Vibration Isolation - FOR PRINT.pdf ]
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lecture_notes: [ ./lecture_notes/Isolation 7.pdf ]
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exercise_sheets:
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- ./exercise_sheets/Vibratioon SHEET 7 - Isolation Part I.pdf
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- ./exercise_sheets/Vibratioon SHEET 7 - Isolation Part I - Solutions.pdf
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- ./exercise_sheets/Vibratioon SHEET 7 - Isolation Part II.pdf
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- ./exercise_sheets/Vibratioon SHEET 7 - Isolation Part II - Solutions.pdf
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---
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Vibration isolators are used to reduce the vibration transmitted from a source.
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They work by introducing flexibility between a device and its support.
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There are a two potential aims for vibration isolation:
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1. Reduce force transmitted to the support (e.g. a passing train that vibrates the ground)
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1. Minimise displacement transmitted to the device (e.g. a satellite mounted in its launch vehicle)
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# Types of Isolators
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- Elastomeric --- most common type of isolater
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- Pneumatic
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- Coil spring
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# Transmissibility Analysis
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Isolators tend to be much more flexible than the devices they support.
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A good first approximation is to use a single degree of freedom model:
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- the device to be isolated is treated as a rigid body
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- the isolators are represented by a spring-damper combination
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- steady-state harmonic response is used to characterise the isolation performance at different frequencies
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Derivations for force and displacement transmissibility equations are in lecture slides (p. 6-11).
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It is always best to derive $T_D$ and $T_F$ for each system.
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The aim when selecting isolators is to ensure that the system operates in the isolation region:
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# Isolation Efficiency
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$$\eta_\text{isolation} = 1-T$$
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# Isolator Selection
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- to reduce vibrations, $\omega_n << \omega_\text{min}$
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- $m$ and $k$ determine $\omega_n$
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- $k$ is given by the isolator
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- the mass supported by the isolator can be increased by mounting it on an inertia base.
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- for most commercial isolators, $\gamma < 0.$ (it is normal to assume zero damping)
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- it is also normal to treat each isolator independently of the others
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## Maximum Static Deflection
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Manufacturers often specify a maximum static deflection, where the spring will not behave linearly:
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$$X_0 = \frac{g}{\omega_\text{min}^2}\left(1+\frac{1}{T_\text{max}}\right)$$
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## Design Procedure
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1. Find centre of mass of the machine
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1. Select number and position of attachment points for isolators
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1. Estimate load supported by each isolator
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1. For each isolator position
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1. Calculate maximum stiffness
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1. Select isolator with lower stiffness
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1. Check that this does not exceed static deflection limit
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