1. Lecture 3: Vibration in Transport presented by David Shires
Packaging Dynamics
Lecture 3: Vibration in Transport presented by David Shires
Editor-in-Chief, Packaging Technology & Science
Chief Consultant, Pira International

2. In the last lecture we talked about frequency domain
We can use the frequency domain to understand transport vibration

3. Power Density Spectrum (psd plot)
Power Density g2/Hz
Frequency Hz

4. Power Spectral Density
Imagine listening to white noise through a filter
White noise is a random wave and contains equal power at all frequencies
The narrower the filter’s bandwidth the quieter the noise
The wider the filter’s bandwidth the louder the noise
We can only quantify volume as a function of bandwidth
Even if we don’t filter the noise our hearing, or the speakers, have a bandwidth.

5. Power Spectral Density
In transport vibration we are interested in acceleration and power
power is the equivalent of volume in sound
power relates to the work done on a package
Power ά (acceleration)2
We can only quantify power in terms of bandwidth
We are interested in which frequencies of the vibration have high power - we chose a narrow bandwidth – 1Hz
Our unit of power spectral density is g2/Hz

6. The lowest frequency we can determine:
= 1/t Hz
We can do a FT to show the frequency content of our random vibration
We can do it over a short or longer period
For a whole record we usually average a series of periods

7. Shock in Time Domain Examples Half sine 50G shock pulse
3.2 ms duration
Magnitude
Shape
Duration

8. Shock in Time Domain How do we describe the white shock pulse?
Which pulse is most damaging?

9. Shock in Frequency Domain
We can do a FT on the shock pulse:
Show us the power spectral density
We need also to understand the response of the product or product and pack
These are damped mass springs
We can combine the FT with the frequency response

10. Shock Response Spectrum10 20 30 40 50 60 1 2 3 4

11. Shock Response Spectrum10 20 30 40 50 60 1 2 3 4

12. Shock Response Spectrum
Describe a complex shock by its SRS
Synthesise a (simpler) shock giving the same SRS

13. Shock Response Spectrum
Depending on the SRS of the product’s components:
The peak acceleration of the components might be higher or lower than that of the cushion
Shock inside product depends on SRS of pulse and natural frequencies of product. It is often higher than at cushion

14. Vibration in Transport
Modes of Transport
Road
Rail
Sea
Air
Many variables within each mode

15. Road Transport

16. Road Transport
Air sprung
Leaf Sprung
Number of axles
Load

17. Road Transport Road surface Road Condition Tyre pressure & quality
Tar / concrete / laterite /gravel / unmade
Road Condition
Tyre pressure & quality
Load

18. Road Transport Trailer base and chassis structure Position Size Load
Steel
Timber on steel
ISO container
Position
Middle or rear
Deck
Chassis
Size
Load

19. Road Transport For a given truck and load
the power spectrum remains the same overall shape
but varies in power with:
Speed
Road quality
Position on truck bed

20. Road – Load in Truck

21. Position in Truck

22. Speed

23. Speed

24. Tyre Pressure

25. Axis

26. Data over time

27. Sampled Data

28. Continuous Data

29. Simplified PDS

30. Air Sprung Motorway

31. Steel Sprung Motorway

32. Air Sprung – Mixed Roads

33. Steel Sprung Mixed Roads

34. Steel Sprung Very Rough Roads

35. Jet Aircraft

36. Propeller Aircraft

37. Sea – ISO Container

38. Sea State