Position: In this page, the theoretical and practical background for the development of a highly stable and sensitive weighing system is discussed .The loaded end of a loadcell will undergo bending and this change in dimension is measured as "strain" using strain gauges fixed to the loadcell. This scheme needs precise electronic arrangements to make up for the inherent variations of the strain gauge. In the present work, the deflection of the loaded end of a cantilever is measured as an axial misalignment between two multimode fiber end faces. The optical power coupled to the receiving fiber is proportional to the deflection of the loaded end of the loadcell. This can be easily detected by simple and effective optical detection methods
1. INTRODUCTION
For the measurement of force, vibration and weight by electronic means, we usually make use of a weighing system that has a loadcell and a collection of four strain gauges as the basic unit. In this weighing system, the applied load (force) will produce a change in the loadcell dimensions that will be transferred to the bonded strain gauges that in turn will produce a change in resistance that is measured by means of Wheatstone's bridge [10]. Even though this system is widely used it has several disadvantages such as, electromagnetic noise due to its electrical nature which affects the strain gauge and hence the output. Another major problem is the self heating of the gauge. To eliminate this, complex arrangements are employed. Another parameter of prime concern with electrical strain gauges is that these gauges are to be hermetically sealed and bonded to the loadcell body or else this will lead to earth leakage resistance and thereby affect the final outcome. To overcome the above fact the weighing load cell system is fabricated with utmost care. Also, the electronic circuits that are employed for detection, manipulation and read out have to be highly error free and this makes the system more complex. In the present study a weighing unit has been developed without any strain gauges being used, instead the dimensional change of the loadcell body is measured by the axial misalignment of two identical multimode fiber end faces .
2. THEORY OF OPERATION
In a cantilever type loadcell, one end is fixed firmly to a rigid support and the other end where the unknown force is applied is free. The applied force can be determined either by measuring the strain undergone by the loadcell at the fixed end, or by measuring the deflection suffered by the free end of the loadcell. In usual practice, four strain gauges are bonded to the load cell-two on top and two at the bottom of the loadcell body near the fixed end. Maximum strain is felt at the fixed end and maximum deflection is felt at the free end. Hence either strain () or deflection () of the free end can be measured as a function of applied force.
For a given force "F" the strain () at the fixed end is given by the relation [10]
Where, "F" is the force applied, "E" the Young's modulus of the bar, "L" the length, "b" the breadth and "t" the thickness of the bar. Also, at the free end, the deflection () is given by the relation .
Where lat is the coupling efficiency under axial misalignment, given by the relation .
In the present work, the deflection at the free end is measured as a function of the axial misalignment of two fiber end faces. When two fiber end faces are aligned axially and one fiber is coupled to an optical source (LED), the power obtained at the other end of the second fiber [8] will depend on several parameters such as the numerical apertures of both the fibers, their core radii, the length of each fiber and finally on the extent to which they are axially aligned. In the present weight system we made use of two identical fiber pieces, so that all fiber related parameters are identical for the transmitting and receiving fibers. Now, the only parameter that will affect the amount of optical power at the farther end is the axial alignment. A simple relation connecting input optical power and the optical power at the farther end is given as.
Where △y is the lateral offset between the axes of two fibers and "a" is the core radius. From (3) and (4) it is clear that the output optical power at the farther end will be at a maximum when △y = 0 i.e. when there is no lateral misalignment. It also implies that the output power will decrease as we move away from the axial position. Finally, we can relate the deflection of the free end of the loadcell where one of the fibers is attached firmly and the output optical power as.
3. SYSTEM DETAILS
To measure the deflection of the free end of a load cell by the optoelectronic method, initially one end of the load cell body is firmly fixed on a vibration free arrangement and then a suitable length of multimode plastic fiber is cut into two equal pieces and one piece is glued to the free end of the loadcell. The end face of the fiber is polished by suitable materials. The second piece of fiber is fixed on a rigid post that is capable of fine position adjustments in all three directions. The second fiber is aligned axially in such a position that the detector gives the maximum output, according to the above mathematical relations. A detailed sketch of the experimental setup is given in figure 1.
Fig. 1 : Experimental setup
The source used in this weighing system is an ordinary available LED. It was excited from a constant current source [10] and helps to maintain the output optical power from the source and kept it stable to a certain extent. But since this arrangement alone will not help to overcome the inherent fluctuations of the LED source, a new technique has been employed by developing a dual coupler for coupling two fibers to a single source, one being the sensing arm and the other one the reference arm. Outputs of these two fibers are detected using identical photodiodes which feed to the inputs of a differential amplifier [10] weighing system. This arrangement helps to cancel the intensity fluctuations of the source and the output voltage of the amplifer will depend only on the contribution of the sensing arm.
To study the deflection in accordance with applied force the free end of the loadcell was loaded with known weights. The output power was noted at every loading and unloading and the mean value of output for that load was normalized and plotted against a load. As expected and supported by the relations, the graph shows excellent linearity and repeatability.
5. RESULTS AND DISCUSSIONS
The graph in figure 2, connecting load variation and its corresponding output power shows a good linear relationship suggesting that this weighing system can be effectively employed for measuring force, vibration and weight without the usage of any electrical strain gauges. This system measures the deflection of the loaded end optically; hence, the problem of creep, need for hermetically sealed bonds, and electromagnetic noise contribution etc can be easily avoided. This weighing system is more effective than ‘current’ concepts using strain gauges.
Fig. 2 : Response of the fiber optic based weighing scheme for increasing loads
REFERENCES
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P. Benjamin Varghese*, Satish John and K.N. Madhusoodanan
Department of Instrumentation, Cochin University of Science and Technology, Cochin *E-mail : benjamin@cusat.ac.in
