We Stand Below Our Work
BDI Cable Force Measurement System
Description
The BDI Cable Force Measurement System was designed for engineers to easily determine tension forces in several cables at one time. In many situations, the advantage of this approach is that while the force in one cable is adjusted, the forces in the remaining cables can be monitored in real time. This allows for much more efficient force adjustment procedures when compared to taking one set of readings with a single-channel system, making adjustments, and going back and making individual readings again. The single channel approach requires the operator to manually record the information, leading to the possibility of making mistakes, especially when large numbers of force measurements are required.
BDI Cable Force Measurement System (BDI-CFMS)
The BDI system consists of a programmable datalogger that is capable of reading and recording the output of up to 10 accelerometers at approximately 100Hz. A standard notebook-sized PC is connected to the logger and the force measurements from all of the accelerometers are automatically calculated, updated, and displayed. In addition, the percent difference from the target load (the average of all forces) is displayed as well in terms of “plus or minus”, allowing the engineer to quickly determine which cables should be tightened or loosened. BDI custom-configures the software and hardware for each cable force system depending on the number of channels required. Hardware specifications are supplied with this system description.
The general principal of operation is based on the well-known behavior of a vibrating wire or string. Using this concept (in this case, a large cable), it is possible to calculate the cable force given its mass, length, and natural frequency of vibration. The first two quantities are readily available based on the cable's physical characteristics. The cable force can then be calculated from the natural frequency of transverse vibrations from the following equation:
where:
T = tension force in the cable.
f = frequency of vibration at the nth mode.
L = effective cable length.
μ = weight per unit length.
g = gravity constant of acceleration.
n = mode number associated with the specified natural frequency.
Use of Equation 1 requires that units of measure be consistent. In the program, the value of gravity is defined in terms of feet per second squared, so it is required that the cable length be defined in feet and the unit length of cable be one linear foot. The units of force must be the same for the cable tension and weight per linear foot. It is recommended that all user input be defined in terms of feet and pounds force.
Since it is of interest to determine the natural frequencies of the cable, an acceleration measurement made on the cable while it is vibrating can be converted to the frequency domain by using a Fast Fourier Transformation (FFT) algorithm. An FFT determines the signal magnitude associated with a given frequency. A typical acceleration signal is shown in Figure 1 and shows the magnitude of acceleration as a function of time. Figure 2 illustrates the same acceleration record transformed into the frequency domain after being run through an FFT algorithm. It is observed that the FFT plot is composed of a large number of equally spaced peaks, each of which occurs at a frequency associated with a natural vibration mode. The distance between each peak is equal to the fundamental frequency.
Once these frequency response records are obtained, it is a relatively simple process to determine the fundamental frequency of the cable, either graphically or numerically as follows:
- Determine the frequency with the largest magnitude.
- Calculate an approximate fundamental frequency by finding the next peak in the FFT record and computing the difference.
- Compute the mode number associated with the largest peak by dividing its frequency by the approximate fundamental frequency and rounding the result to the nearest integer.
- Obtain an accurate value of the fundamental frequency by dividing the frequency associated with the largest peak by its associated mode number.
The resulting value of the fundamental frequency can then be used in Equation 1 to determine the force in the cable. The accuracy of the frequency response and mode calculation is critical because the force in the cable is dependent on the square of the fundamental frequency. The resolution of the FFT plot improves with the length of the test relative to the sampling rate, so it is best to record as long of a data record as can be conveniently processed.
Figure 1 Acceleration Record in Time Domain
Figure 2 Acceleration Record in Converted to Frequency Domain