Natural frequency of vibration gives precise tension in wires

Tom Shelley reports on a device that makes precise the measurement of tension in rods and wires from their natural frequency of vibration By striking rods and wires under tension, and extracting their fundamental natural frequency of vibration, it has proved possible to develop a hand held instrument capable of accurately determining the tensile forces applied to them. Although simple in theory, the low frequencies - Hz to a few tens of Hz, and complex sound spectra have hitherto prevented their accurate analysis. A new sampling and statistical computation method has now overcome the problems, and work is underway to extend the method to determining tension in lift cables, racing yacht rigging and other items. The development started when a customer asked TMS Systems, which makes cable tensioning equipment, if they could come up with a non-contact method for determining the tension in reinforcing cables and bars for pre-stressed concrete beams. They, in turn, consulted Applied Measurements of Aldermaston, makers of precision load cells. Peter Lewis, the managing director of Applied Measurements then went to Colin Paterson, a local consultant, who came up with the idea of measuring vibration frequencies from the effect that a vibrating steel bar would have on an externally applied transverse magnetic field. After two years development, this has led to a new instrument, the 'Digiforce', based on a novel patented hardware technique and mathematical analysis process. The end of the hand held device has a permanent magnet, in the centre of which is a Hall effect sensor. In use, the instrument is first programmed with the length of the bar or cable whose tension is to be measured, and its weight per unit length. It is then placed with the sensor close to the bar. The measurement process is triggered, and the bar struck with a mallet. After a few moments, the tension appears on the LCD display on the instrument Lewis demonstrated on a 4m test rig, that if the tension is very low, so that the steel only produces a dull thud when struck, the instrument produces erroneous values. It is also apparently important that the instrument be held still during measurement, to eliminate Doppler errors, and that the steel be struck with the mallet, or even the hand, but not with a steel hammer or spanner. Provided this is done, accuracy is about 1 to 2%. Tensions in stainless steel or other non ferromagnetic wires can be measured by attaching clips made of ferromagnetic materials, provided their masses are insignificant compared with that of the cable or rod. It is clear, even to the untrained ear, that the vibrations being analysed are very complex. The fundamental frequencies that the method depends are in the range, 3Hz to 70Hz, and not the metallic note heard by the ear. The tension is determined from the simple formula, T = 4 x length2 x Hz2 x weight per unit length. The patent, however, explains that the method used to determine the frequency is quite complicated. Because of the very low frequencies, tuned circuit filter methods are not an option. Instead, the device makes an initial 20 measurements of the times taken for each oscillation, and throws these away. The next five measurements from 10 oscillations are then used to establish a tolerance band, to establish which measurements should contribute to the computation, and which should be rejected as spurious. Subsequent measurements are then made, and those that fall within the tolerance band are used to compute the final value to the required accuracy. The computational algorithms are in fact even more sophisticated than this, with various try again loops if things don't work right the first time around. We suggest that if anyone among our readers is seriously interested in the details, they should get in touch with the company and read the patent themselves. This summarises the circuitry and the algorithms used but still covers some 12 pages. Because the main business of Applied Measurements is in making and supplying precision load cells, and such load cells are used as calibration checks on the Digiforce units, the instrument made measurements are traceable back to NPL standards. The present device is the result of customer beta tests on the first six pre-production units. One of the results of this test programme is that the production version includes on-board logging, and an RS232 port to allow data downloads. This is protected from the environment by the same cover used to protect the PP3 battery. The current sales price is £1,450, including carrying case and all accessories. Present customers include Bison, Concrete, Tarmac, RMC and other blue chip construction companies. Following the success of the Digiforce, other potential customers are now coming forward who want to make non contact measurements of loads on lift cables, yacht rigging, cables used to support leading edge buildings, and anchor chains in the North Sea. Here there is a snag, since end shackles have a significant impact on natural frequencies of vibration, mainly because of their additional mass. However, nothing daunted, a development programme is now under way to produce instruments to meet these particular needs. Without going into details, it will require making measurements at more than one loading, in order to calibrate the system and allow the mathematical elimination of the extra variables. However, in systems that are the same or identical this should only be need to be done once. For the racing yacht industry, Peter Lewis has come up with a special possible design, based on a totally different working principle, but we are unable to describe this here, because it has yet to be patented. However, having got into the field of developing innovative ways of measuring loads, we can expect other new products. Accurately measuring the liquid content of filled vessels or their working pressure from natural frequency of vibration with non contact instruments offers further possible applications and challenges for the base technologies. Applied Measurements Eureka says: The accurate determination steel cable tension by monitoring natural vibration frequency has opened up a whole possible new technology for non contact measurement of stress, strain and content of process vessels. Pointers * Instrument accurately measures tensile stress in a steel cable or bar from its natural frequency of vibration * Instrument is non contact, detecting changes in an externally imposed magnetic field caused by movement of the metal * Accuracy is 1 to 2%