Page 78 - Instrumentation Reference Book 3E

Practice of length measurement for industrial use 63

in an a.c. bridge to which phase-sensitive detection trolled machine tools. A form of long inductive
is applied in a similar manner to recover a polar- sensor that has stood the test of time is the flat,
ized d.c. output signal. “printed” winding that is traversed by a sensing
Inductive sensors of the mutual-inductance short, flat coil. Each cell of this continuous grid
form are manufactured in a vast range of sizes comprises a coil pair overlapped by the sense coil
providing for length detection from as small that forms a flat profile LVDT form of sensor.
as atomic diameters (sub-nanometer) out to a Angles can be measured electromagnetically
maximum range of around 1-250mm. They are using devices called Synchros. These inherently
extremely robust, quite linear, very reliable, and include means for transmitting the information
extremely sensitive if well designed. By mounting to a distance and are therefore described under
the core on the measured value object and the Telemetry in Part 4.
body on the reference frame it is also possible to
arrange for non-interacting, non-contact meas-
urement. Frequency response depends upon the 3.5.3.3 Electrical-capacitance sensors
carrier frequency used to modulate the coils; gen- Electrical capacitance stores electrical energy in
eral practice sets that at around 50 kHz as the the electric field form; electrical inductors store
upper limit, but this is not a strong constraint energy in the magnetic field form. Electromag-
on design. Attention may also need to be paid netic theory relates the two forms of field and
to mechanical resonances of the transducer. thus most concepts applied to magnetic-induct-
The slecond class of magnetically inductive ance sensing are applicable to electrical-capacit-
length sensors, the magneto-electric kind, are ance structures.
those in .which part of the electromagnetic circuit It is, therefore, also possible to sense length
moves to generate a voltage caused by flux-cut- change by using the input length to alter the
ting. For these the relevant basic expression is structure of a capacitance assembly or to cause
e = -(N d6ldt) where e is the voltage generated shape change to a solid naterial, thereby directly
as N turns are cut by flux 4 in time t. These are generating charge. The electrical capacitance of a
strictly velocity, not displacement sensors, for the structure formed by two electrically conducting
output is proportional to velocity. Integration of plates is given by
the signal (provided it has sufficient magnitude to
be detected, for at low speeds the signal induced
may be very small) will yield displacement.
This form of sensor is covered in more detail in where C is the capacitance, E the dielectric con-
Chapter 6. stant of the material between the plates in the area
Magneto-electric sensors are prone to stray A where they overlap at a distance of separation 1.
magnetic field pick-up for that can introduce Thus a length sensor can be formed by varying
flux-cutting that appears to be signal. Good the value of I which gives an inverse relationship
shielding is essential to reduce effects of directly between length input and capacitance change or
detected fields and also for the more subtle by varying one length of the two plates that com-
induced eddy current fields that are produced in bine to provide the overlap area A; this latter
adjacent non-magnetic materials if they are elec- alternative can give a direct relationship. It is also
trically conducting. Magnetic shielding is a highly sometimes practical to vary E by inserting a mov-
developed engineering process that requires spe- ing piece of different dielectric into the capacit-
cial materials and heat treatments to obtain good ance structure.
shielding. Manufacturers are able to provide Simpler forms make use of a single capacitance
units incorporating shielding and to advise users structure, but for these, variation in E can intro-
in this aspect. It is not simply a matter of placing duce error due to humidity and pressure changes
the unit im a thick, magnetic material case! Herceg of air, the most commonly used dielectric. Differ-
(1976) is a starting point on effective use of LVDT ential systems are more satisfactory. Figure 3.14
units and other inductive sensors. shows the basic configuration of differential
When larger range is required than can be con- capacitance sensors. They can be formed from
veniently accommodated by the single unit flat plates or from cylindrical sections, whichever
(desired discrimination will restrict range to a is convenient. The cylindrical form of the second
given length of basic cell) it is possible to add design has been used in a highly accurate alter-
inductive sensor cells, end-to-end, using digital native to the LVDT. The guard rings shown are
logic to count the cells along the interval with not needed if some non-linearity can be accepted.
analog interrogation of the cell at the elid of the Capacitance systems are characterized by high
measured value interval. This hybrid approach output impedance, need for relatively high excita-
was extensively developed to provide for the tion voltages, accuracy of plate manufacture, and
meter distances required in numerically con- small plate clearance dimensions.