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Handbook of Railway Vehicle Dynamics

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428<br />

Relative Sensitivity<br />

30<br />

dB<br />

20<br />

10<br />

0<br />

− 10<br />

− 20<br />

− 30<br />

Useful Frequency Range<br />

10% limit 0.3 f m<br />

3dBlimit 0.5 f m<br />

Main Axis Sensitivity<br />

Transverse Sensitivity<br />

− 40<br />

0.0001 0.001 0.01<br />

<strong>Handbook</strong> <strong>of</strong> <strong>Railway</strong> <strong>Vehicle</strong> <strong>Dynamics</strong><br />

Transverse<br />

Resonance<br />

Frequency<br />

Proportion <strong>of</strong> Mounted Resonance Frequency<br />

Mounted<br />

Resonance<br />

Frequency<br />

f m<br />

0.1 1 10<br />

FIGURE 13.5 Frequency response <strong>of</strong> an accelerometer (courtesy <strong>of</strong> Bruel and Kjaer). Source: From<br />

Serridge, M. and Licht, T. R., Piezoelectric Accelerometers and Vibration Preamplifier <strong>Handbook</strong> Bruel and<br />

Kjaer, Revised November 1987. With permission.<br />

will be dictated by the resonant frequency<strong>of</strong>the accelerometer. Acommonly used rule<strong>of</strong>thumb is<br />

that the upper frequency limit shouldbenomore than one third <strong>of</strong> the resonant frequency. Forgeneral<br />

purposepiezoelectric accelerometers, the resonant frequencymay be <strong>of</strong> the order <strong>of</strong> 20 kHz, putting<br />

their upper useable limit way above anything likely to be requiredfor avehicle dynamics application.<br />

Piezoelectric accelerometers have one very important limitation with regard to vehicle dynamics test<br />

applications. Thelower frequency limit is determined not by the accelerometer itself but by the RC<br />

time constant <strong>of</strong> the charge amplifier used to condition the signal from the transducer. Whilst it is<br />

possible tosense very low frequencies using preamplifiers with very high impedance, general<br />

purpose equipment may limit the lower useable frequency limit to 1–3Hz. Clearly, this has<br />

important implications for the vehicle dynamics engineer. A general purpose piezoelectric<br />

accelerometer may be quite acceptable for mounting on unsprung masses such as the axle box, but<br />

may be operating near its lower limit when mounted on abogie frame. <strong>Vehicle</strong> body modes may<br />

occur at 0.5 Hz or less and therefore would be below the lower limit <strong>of</strong> ageneral purposepiezoelectric<br />

accelerometer. Piezoelectric accelerometers are generally not capable <strong>of</strong> measuring the quasi-static<br />

accelerations due to curving. In the case <strong>of</strong> bogie and body measurements, the capacitive<br />

accelerometer, described in Section II.B.2 below, will provide asolution to this problem.<br />

An ideal accelerometer design would only respond to vibrations applied to the main sensing<br />

axis. However, in practice, mostaccelerometers will exhibit somesensitivity to excitations at 908 to<br />

the main axis, known asthe transverse sensitivity. These are caused bysmall irregularities in the<br />

piezoelectric material causing the axis <strong>of</strong> maximum sensitivity to be slightly misaligned with the<br />

operating axis <strong>of</strong> the accelerometer. It can be imagined, therefore, that the transverse sensitivity will<br />

not be constant and subsequently there will be directions <strong>of</strong> maximum and minimum sensitivity at<br />

908 to each other. Some accelerometer designs will indicate the direction <strong>of</strong> minimum transverse<br />

sensitivity on the accelerometer body to aid correct mounting <strong>of</strong> the device. It is generally found<br />

that the transverse resonant frequencyislower than the main resonant frequencyand therefore falls<br />

within the useable bandwidth <strong>of</strong> the accelerometer. However, at the relatively low frequencies <strong>of</strong><br />

interest to the vehicle dynamics engineer, the maximum transverse sensitivity is usually less than<br />

4% <strong>of</strong> the main axis sensitivity. 4<br />

© 2006 by Taylor & Francis Group, LLC

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