56 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



where n x is the number of turns of the primary coil, i the instantane- 

 ous primary current, and x the distance between the primary coil and 

 the coil image (i.e., twice the distance between the coil and the metal 

 plate) . For rjr p = 1 , the value dM/dx can be found from Fig. ( 1 -2) 36. 

 For i = 1 amp, n = 12, and for x = r v , the force is of the order of 

 10 dynes. A force can also arise between the primary and the second- 

 ary coil but is usually negligible if the current in the secondary coil is 

 small. 



Little information is available as to the accuracy of the method. 

 Considering the difficulty of measurements at radiofrequencies, the 

 error may be estimated to be 1 to several per cent. 



The calibration curve is essentially nonlinear. Over a limited 

 range approximate linearity can be obtained. The linearity over a 

 selected range of displacement can be improved by increasing the 

 radius r p of the primary coil and by decreasing the ratio of the radii of 

 secondary to primary coil rjr v , although such a procedure diminishes 

 the sensitivity of the transducer. 



The dynamic response is primarily limited by the frequency of the 

 applied current, which is usually in the megacycle range. Mechanical 

 oscillations in the range from 10 to 20,000 cps have been measured 

 with the eddy-current transducer. 



The transducer is insensitive to lateral shifts between the coil 

 system and the metal plate, but errors are likely to occur from non- 

 parallelism between the coil planes and the metal plate. 



For references, see J. Obata, J. Opt.Soc. Am., 16, 419 (1928); H. A.Thomas, 

 Engineer, 135, 138 (1923); H. A. Thomas, J. Scl. Instr., 1, 22 (1924). 



d. Magnetoelastic or Magnetostrictive Transducers. The magnetic 

 permeability of ferromagnetic materials changes in general when the 

 material is subjected to mechanical stress (Villari effect). The per- 

 meability can increase or decrease, depending upon the material, the 

 type of stress (compression, tension, or torsion), and the magnetic 

 flux density in the sample. Examples for the relationship between 

 the flux density and the applied stress for iron are shown in Fig. 

 (1-2)37; the values reported in the literature vary widely. The mag- 

 netic permeability of nickel increases when the probe is subjected to 

 compression and decreases when subjected to tension. The general 

 trend of the characteristics for nickel is illustrated in Fig. (1-2)38. 

 The response to torsion of a magnetoelastic nickel probe is shown in 

 Fig. (1-2)39, curve a; the flux density increases as the angle of 

 torsion increases, regardless of the direction of rotation. A strong 

 hysteresis effect is noticeable. If a constant longitudinal tension is 



