WO1997039312A1

WO1997039312A1 - Displacement sensors

Info

Publication number: WO1997039312A1
Application number: PCT/GB1997/001041
Authority: WO
Inventors: Donald Lionel Hore
Original assignee: Regal Components Ab
Priority date: 1996-04-15
Filing date: 1997-04-15
Publication date: 1997-10-23
Also published as: GB9607750D0

Abstract

An inductance displacement sensor comprising an array of progressively wound coils (61) extending along a path, and an inductance anomaly element (62) displaceable along the path and being dimensioned so as to affect the inductance of only a part of the coil array at any one time; the progressive nature of the coil array having the effect that the amount of the increase or decrease in inductance of the affected part varies in magnitude with the location of the affected part along the array. In a form which is particularly suitable for manufacture using printed circuit techniques, the coil array (61) comprises a single flat coil wound as a single elongate eccentric spiral, elongate in the path direction, and eccentric so that there is a high turn density at one end region, progressively decreasing towards the other end region. A pair of such coils may be placed together in opposite orientations and connected in series.

Description

DISPLACEMENT SENSORS The present invention relates to inductive displacement sensors. It is primarily concerned with sensors for linear displacement, but is also concerned with sensors for nonlinear (particularly angular and rotary) displacement.

In one aspect the present invention provides an inductive displacement jensor comprising an array of progressively wound coils extending along a path, and an inductance anomaly element displaceable along the path and being dimensioned so as to affect the inductance of only a part of the coil array at any one time; the progressive nature of the coil array having the effect that the amount of the increase or decrease in inductance of the affected part varies in magnitude with the location of the affected part along the array.

In one form of embodiment the sensor comprises an array of unequal coils connected in series, and an inductance anomaly element displaceable relative to the array of coils and dimensioned so that at any one time it principally affects the inductance of only a subset of coils (preferably only a single coil) to which it is at that time adjacent, the inequality of the coils being such that the inductance of the whole array is different depending on which subset is affected.

Preferably there is an array of equal coils which are each divided into first and second sub-coils, the first sub-coils being mutually unequal and being serially connected to constitute a first said array of unequal coils; the second sub-coils correspondingly being mutually unequal and also being serially connected to form a second said array. Preferably the first array is in series with the second array and means are provided for monitoring the voltage drop across one series. Preferably all of the sub-coils are homopolar with the corresponding sub-coils.

Preferably the coils are arranged as salient poles, their axes intersecting- the intended relative displacement path of the inductance-affecting means. In a preferred type of embodiment there is a ferromagnetic core member of C-section, one arm being divided into core portions on which the coils are wound. The coil axes extend across the gap towards the other arm so that a flux circuit for each coil can extend around the C- section and across the gap. The displacement path may then extend within the gap.

In a second form of embodiment which is particularly suitable for manufacture using printed circuit techniques, an array of progressively wound coils comprises a single flat coil wound as a single elongate eccentric spiral, elongate in the path direction, and eccentric so that there is a high turn density at one end region, progressively decreasing towards the other end region. A pair of such coils may be placed together in opposite orientations and connected in series.

The inductance anomaly member may be ferromagnetic (thus increasing inductance) or screening (i.e. a non- ferromagnetic conductor) (thus decreasing inductance) . Alternatively it could be an absence: that is, there could be a relatively large (ferromagnetic or screening) member which affects the inductance of every coil (or part) except for a part or subset adjacent a gap in the member.

In a second aspect the invention provides a displacement sensor having a first elongate element having a wound portion, and a second elongate element comprising electrically conductive and/or ferromagnetic material and of length substantially equal to the wound portion, said elements being relatively displaceable in their direction of elongation to vary the proportion of the wound portion which is adjacent the second element. Desirably the range of displacement is substantially equal to the length of the wound portion, from a first configuration in which the wound portion and the second element are substantially in register to a second configuration in which they are substantially out of register. Desirably either the wound portion or the second element is tubular and the other one of them is displaceable within the tube. Generally the elements and the displacement path will be linear, though arcuate versions are also possible.

The wound portion may comprise a plurality of coil portions with taps between them. Signal processing means may be coupled to the taps to detect the relative variation of the inductances of the coil portions, thereby to determine the relate positions of the two elements.

Alternatively or additionally, the inductance of a single winding extending over the whole length of the wound portion may be monitored.

In this second aspect the invention further provides a control system including such a sensor arranged to provide information about relative displacement of components. The components may be a piston and piston rod.

Some embodiments of the invention will now be described with reference to the accompanying drawings in which: - Fig. 1 is a coil connection diagram for explaining the principle of one type of embodiment;

Fig. 2 is a perspective view of a linear embodiment of the invention;

Figs. 3a and 3b are an axial section and a front elevation of a rotary embodiment;

Fig. 4a shows a progressive coil manufactured on a flat substrate e.g. a p.c.b.;

Fig. 4b shows a winding of a variant of the Fig. 2 embodiment employing a progressive coil; Fig. 5 shows a sensor employing a pair of coils as shown in Fig. 4a: Fig. 5a is a side view, Fig. 5b is a plan view, and Fig. 5c is a schematic circuit diagram;

Fig. 6 shows how flexible coils of the Fig. 4a type 5 can be conformed to a piston-and-cylinder, Fig. 6a being an axial section and Fig. βb being an end view;

Fig. 7 shows an interleaved array of oppositely handed coils of the Fig. 4a type; Fig. 8 shows a rotary machine having sensor coils applied inside a- rotor housing;

Fig. 9 shows a pair of progressive coils extending arcuately;

Fig. 10 shows a multilayered linear coil array; Fig. 11 is a graph of voltage versus stroke;

Fig. 12a shows two pairs of series coil assemblies for providing 2-channel output data;

Fig. 12b is a schematic circuit diagram corresponding to Fig. 12a; Fig. 13 is a graph of voltage outputs versus displacement for the Fig. 12 device;

Fig. 14 shows a sensor embodying the second aspect of the invention: Fig. 14A is a schematic sectional view of the sensor; Fig. 14B is an end view of the core of the sensor; and Fig. 14C is a schematic view of the core winding;

Fig. 15 is a graph illustrative of the operation of the Fig. 14 sensor;

Fig. 16 is a schematic sectional view of a fluid- power cylinder assembly having a control system that uses a sensor embodying the second aspect of the present invention,-

Fig. 17 is a schematic view of a second embodiment of a sensor of the second aspect;

Fig. 18 is a graph illustrative of the operation of the Fig. 17 embodiment;

Fig. 19 is a schematic view of a third embodiment of a sensor of the second embodiment; and

Fig. 20 is a schematic view of a control valve assembly including a fourth embodiment of sensor of the second aspect.

Fig. 1 shows an array of ten solenoidal coils 1-10 made up of two separate, windings A-B, B-C connected in series, and wound to develop flux in the same direction, i.e. of the same polarity. The particular characteristic of the winding arrangement is the distribution, which gives progressive sharing between the two windings from one end to the other, while maintaining the same total number of turns in each coil. Thus, winding A-B occupies 100% of coil 1, 89% of coil 2, and so on down to 11% of coil 9 and 0% of coil 10. Winding B-C occupies the corresponding remaining portion of the coils, from 100% of coil 10 down to 0% of coil 1. When an a.c. voltage is applied cross terminals A,C, the voltage at the centre tap B is half the supply voltage, as the coils represent a simple potential divider, with symmetrical halves.

If now a ferromagnetic core 20 is introduced into one of the coils, as indicated at coil 3, the increased permeability of that coil will be reflected in a higher inductance in this one coil, and a higher than average volt-drop across it. This increased volt-drop will however, be shared unequally between the two windings, more of it being in A-B than B-C, so that the voltage between terminals B and C will be lower than that between A and C. Inserting the core 20 in any other coil instead will produce a different change in voltage level at mid¬ point tap B (which, in the absence of the core 20, is half the supply voltage) in proportion to the difference in the share of the coil between the two windings and the difference in inductance of the affected coil from the mean inductance of the remainder.

Note that similar results would be obtained if all the coils had ferromagnetic cores to begin with except one; varying the coil from which the core is removed would then cause a similar change in output voltage at the mid-point tap, but in the opposite direction. It is therefore the presence and location of an anomaly in the flux distribution which provides a change of output; the magnitude and phase sense of this change defines which coil -has the anomaly. Such an arrangement, requiring insertion or removal of cores, is of only limited usefulness as a displacement sensor, but the principle is readily applied by the use of a wound stator having discrete poles in place of the solenoidal coils of Fig. 1, and by arranging for the flux developed by these proportionately-wound poles to cross an air-gap in which a moveable means of permeability variation can travel to produce the required anomaly.

Fig. 2 shows a practical embodiment of the principle for linear displacement sensing. A stator 11 of ferromagnetic material such as ferrite has a cross- section approximating in shape to an inverted letter G; the vertical section of this core is divided along its length into ten discrete poles P1-P10 each of which carries coils wound as shown by the start of winding A-B which are divided to progressively reduce the share of A- B and increase the share of B-C, as described above, while retaining nominally equal total numbers of turns. (Practical design considerations may affect the precise winding detail and distribution according to the output characteristic desired) .

The flux developed by these wound poles crosses the air-gap to the lower limb of the core, and returns around the back of the core to the poles, as indicated by the broken line at pole Pl. The structure is a three- dimensional magnetic circuit of homopolar form.

An anomaly in the form of a rectangular block of ferromagnetic material 12 is moveable by rod 13 along the stator core. In the position shown it will increase the permeability of the pole P3 to raise the inductance of its windings, thus raising the volt-drop in winding A-C compared with B-C. Linear movement of the block 12 in either direction will transfer the anomaly to different poles, and the precise linear position of the block 12 will be capable of determination from the amplitude and phase of the deviation of the centre-tap voltage from the mid-supply level. Note that the substitution of a block of copper or aluminium for 12 would produce an anomaly in the opposite sense (assuming the applied voltages to be a.c.) , because the screening effect of the eddy currents induced in the metal would reduce the flux crossing the gap, and thus reduce the effective permeability and inductance of pole P3 and its windings.

A particular advantage of this type of embodiment is that the measurable length of traverse is a high proportion of the stator length from a single output channel derived from the voltage at tap B. The converse of this is that the overall length of the linear sensor for a given stroke is dramatically reduced. Up to about 90% of the length can be measured, with no projection of the moving element beyond the stator.

While the Figures show a 10-pole design, this is purely for the purpose of illustration. Similarly, the spread of the anomaly need not be limited to one pole width. The greater the number of poles with a one-pole width anomaly, the greater the proportion of stator length which can be measured. However, this advantage is offset by a reduction in the signal-to-noise ratio, because a small increment of inductance change is represented by a single pole. Reducing the pole numbers, or increasing the spread of the magnetic circuit anomaly, increases the inductance change, and the signal-to-noise ratio of the device.

Fig. 3 shows how the principle can be applied to a practical angle sensor. Ferromagnetic stator 14 is effectively the linear stator of Fig. 2 rolled into a circle, with poles P1-P10 equispaced around its periphery, and carrying proportionately distributed shares of windings A-B and B-C as before. These cause flux to cross an air-gap as indicated by the broken lines.

Passage of the flux from one pole is affected by an anomaly in the form of a ferromagnetic block 15, this being coupled by member 16 to rotate with shaft 17. In the position shown, it increases the effective permeability for pole P3, thus causing a particular voltage phase and amplitude to be detected at tap B. This level will change with rotation, according to the incremental inductance change per pole, and the proportion of the two windings in the anomalous pole. A similar effect in the reverse sense would be achieved by either substituting a block of copper or aluminium for ferrite in the block 15, or by extending the spread of ferromagnetic anomaly 15 to embrace all except one pole, which would then have a lower inductance than all the rest.

Again, the number of poles and the angular spread of the anomaly can be varied at the designer's discretion to meet particular performance requirements.

In all the foregoing embodiments, a conventional electromagnetic machine construction with ferromagnetic core was envisaged. However, the same basic concept of progressively wound coils can be applied advantageously to an air-cored coil construction, which lends itself to economic manufacture using printed circuit techniques. Fig. 4a shows in principle a single coil 61 of this form; it will be apparent that if alternating current is fed through it as indicated, the flux distribution produced will be a maximum at point (a) which has the maximum number of turns surround it, and will be progressively reduced if measurements are taken at points (b) through to (f) . Moving a strip of conducting non-ferromagnetic metal 62 from left to right over these points will reduced the inductance of the coil by its screening effect, as earlier described. The greatest reduction in inductance will be at the left hand end, where most turns are linked, while at the other end the reduction in inductance will be least. In the same way, substituting ferromagnetic material for the metal 62 will increase the inductance by the greatest amount at the left, and by the least amount at the right end. A variable inductance device is thus produced.

Fig. 4b shows how the device of Fig. 2 (which uses individual windings on the different poles) could be adapted to use a more conventional distributed winding arrangement, with a single progressive coil. Fig. 4b shows a progression of four poles so wound; it will be apparent that pole 1 is embraced by all four turns, pole 2 by three, pole 3 by two, and pole 4 by one only of the turns. The rotary embodiment of Fig. 3 could be adapted similarly.

Reverting to Fig. 4a, if an identical coil 63 is mounted facing the first, but with opposite handing, as indicated in Fig. 5, and the two are connected in series with the same a.c. supply, it will be apparent that the strip of screening or ferromagnetic material 62 can now be positioned between the coils to influence their inductance simultaneously. The voltage developed at the common connection point 64 relative to either of the supply terminals 65,66 will then vary with the linear position of the strip 62; This can be moved by means of a rod of non-conducting and non-magnetic material 67 from one end, or similarly from one side by coupling piece 68, to form a linear sensor when suitably housed to hold the coils 61,63 in their correct alignment.

It will be obvious that the coils 61,63 may be etched on printed circuit boards for simple and economic manufacture; it will also be apparent that the degree of linearity of the output characteristic of the device will be a function of the geometry of the progressive spacing of the coils. The linear range of the sensor will be variable according to the length/width aspect ratio of the coils, and the width of strip 62 as in the previous embodiments. There is, however, no need to etch the coils onto rigid circuit boards; flexible substrates may be used instead. This then makes many further variations possible. Fig. 6 shows how two such flexible coils 69,70 can be formed in a curve lengthwise along a tube 71 of rigid non-conducting non-magnetic material, within which a short cylinder or tube of conducting or ferromagnetic material 72 is linearly propelled by a rod 73. This enables the linear sensor to be housed in a similar manner to the well-known ranges of potentiometric and LVDT sensors already established, but with the advantage of much simpler and cheaper winding construction. A further possibility using flexible or rigid printed circuit techniques is to overlay or interweave a pair of coils 61 and 63 of opposite hand over each other to form a single (compound) assembly 74 as shown in Fig. 7. This then enables a moving conducting or ferromagnetic element 62 above the circuit assembly 74 to simultaneously affect the inductance of both coils, and produce a linear displacement sensor as already described, with the added advantage of eliminating wiring between circuit boards. Such a sensing circuit can then be attached to the outer or inner surface of a structure, to enable the position of an externally or internally moved conducting or ferromagnetic inductance-affecting element to be sensed.

For rotary angle sensing, one or more flexible circuits of either singular (Fig. 4) or compound. form (75, Fig. 7) may be attached to the inner circumference of a cylindrical housing 76, (Fig. 8) to sense the angular motion of one or more inductance-affecting elements 62, each attached to a radius arm 77 rotated by a shaft 78 supported by suitable bearings (not shown) . The angular stroke obtainable will then be variable over a wide range, according to the length of circuit 75 in relation to the radius 76. It will also be apparent that circuit 75 could instead be attached to the exterior of 76 to sense the motion of an external inductance- affecting element.

Further rotary sensing constructions can be devised by making the coil tracks follow a radial as opposed to a rectilinear path. Single circuits in pairs or paired compound circuits equivalent to the assemblies 74 of Fig. 7 can then be attached to disc structures as in Fig. 9. Single circuits exceeding 180 degrees span would require facing disc pairs, with a coil on each disc and an inductance-affecting element 62 rotated between them.

With a compound circuit like the circuit 75 of Fig. 7, a single disc only is required, with an element 62 rotated close to its surface. Again, the angular range obtainable is a design variable with the angular spread of the coil assembly.

With spreads below 180 degrees, more than one sensing channel can be accommodated by duplication of circuits and moving elements 62 in either of the rotary forms described. In addition, while the foregoing examples have utilised series auto-transformer connection to effect comparison of inductance, other methods may be used. For example, our current application EP-A-0590830 for a tilt sensing device uses inductance-comparison of two coils in a similar fashion, including connection of the coils separately to capacitors to produce oscillator circuits. With this method, the variation of inductance causes a change of frequency, which may be used to derive a digital output corresponding to displacement.

With the flat coil form described, the number of turns obtainable on a given surface area is inevitably limited. However, overlaying one coil assembly on another of identical layout and connecting them in series will double the effect number of turns, and so on with additional layers. This arrangement may also simplify termination. Fig. 10 shows within bold lines a circuit substrate carrying a coil 61 on the front, while the dotted outline is the same looking through to an identical coil 61 inverted on the back. Fed from outer terminal X on the front, the inner terminals Y of both coils are connected through the substrate, to the outer terminal Z behind. The number of turns has thus been doubled, while external connection is only needed at X and Y. Such paired coils may be used in any of the foregoing embodiments.

All the above has related to sensors capable of producing a single channel analogue output proportional to linear or angular displacement. The demodulated signal is then of the form shown in Fig. 11, i.e. a d.c. voltage level varying with displacement. It is also possible to develop two-channel output data as in the earlier patents to embrace longer strokes by using two pairs of series coil assemblies. This is exemplified in Fig. 12; one pair of series coils 61A, 61B between terminals R,S,T have the form 61 previously described, with coil concentrations at each end of the assembly. The second pair 77A,77B between terminals U,V,W have a form in which the coil concentration is central. Both pairs of coils are simultaneously traversed by induction- affecting element 62 as previously described. If element 62 is conducting, it will have maximum screening effect at the left hand end, to reduce the voltage across R,S. This voltage will rise as 62 is moved to the right, until it reaches the far right hand end, with maximum screening of 61B. Simultaneously ,the screening element 62 is affecting coils 77A,77B, but with peak screening effect displaced by half a coil length from 61A and 61B. As a result, the voltage between terminals ϋ-V will shown a characteristic similar to but displaced from R-S, as in Fig. 13. It will be appreciated that substitution of ferromagnetic for conducting material in 62 will simply reverse the characteristic, by substituting relatively high for relatively low inductance levels. The two- channel data resulting then give two discrete voltage levels corresponding to each position. By suitable geometry of the coils, the characteristics may be made quasi-sinusoidal, so enabling standard sine/cosine resolver-to-digital converter electronics to be utilised. This arrangement of four coils may be adapted to linear or rotary motion sensing as previously described. Although the printed-circuit type of constructions above have no ferromagnetic cores, it is possible to add backing material of a ferromagnetic nature such as ferrite or ferromagnetic particles in a suitable matrix in order to provide a better flux path or to provide screening.

An alternative method of producing a sine/cosine output corresponding with linear motion in a construction suitable, for example, for incorporation in pneumatic or hydraulic cylinders is now described.

Referring now to Figs. 14 and 15, Fig. 14A shows a sensor having a ferromagnetic rod core 105 which, as can be seen from Fig. 14B, has a slot 106 along its length for wiring connections. Most of the length of the core 105 carries a coil winding in four successive sections 107a, 107b, 107c, 107d, which are connected in series to an a.c. supply at terminals V₃ and V₀ (Fig. 14C) . Taps ^T-_LO-' ^τ _bc ^aπ-d T_cd are connected between the coils, so that changes in relative inductances of the coils can be used to produce voltage changes at the taps, as generally described in earlier applications.

Instead of using an inductance influencing moving member of typically half the wound length as in our earlier sensors, a metal tube 108 equal to the wound length is progressively moved over it until it encompasses the whole length. If the tube 108 is ferromagnetic, it will increase the inductance of the covered windings, while if non-magnetic, the eddy currents induced in it will produce opposing flux to reduce the inductance. (A ferromagnetic tube need not be a good conductor - e.g. a tube of a ferrite or ferrite composition. ) Considering first the voltage at the centre tap relative to V₀, this will start at half the supply voltage when the winding is fully exposed, because the impedances of each half are equal. As the tube 108, in this instance of non-magnetic metal, is moved to the left, it will progressively reduce the inductance of coils 107d and 107c, so that the voltage at the centre tap T_bc will rise to a maximum when both coils are screened. Further motion to the left will progressively screen coils 107b and 107a, so that the mid-tap voltage falls again until all coils are screened. Both halves then have equally reduced impedances, so the tap T_bc voltage is again half the supply level. The result is output curve A of Fig. 15 with linear motion.

Considering now the voltage levels at the 1/4 and 3/4 taps T._J., T_cd between coils 107a, 107b and 107c, 107d respectively relative to each other, it follows that the differential voltage will rise to a maximum when coil 107d is screened, because coils 107a-107c share a higher proportion of the supply voltage. As 107c is progressively screened with 107d, the differential voltage will fall, until a minimum is reached when 107b, 107c and 107d and screened. Finally, screening 107a will restore the differential voltage to half the supply when all coils have equal reduced impedance; the result is curve B of Fig. 15.

Because there are now two discrete signals for every position of the tube, absolute position can be determined for the full traverse of the tube over the sensor winding, using circuitry shown schematically as C, which may include an output display e.g. a meter M.

If a ferromagnetic tube is substituted for the tube 108, the general effect will be similar, except that output signals will rise instead of fall, and vice-versa, in comparison with the non-magnetic screening tube.

While the sensor of Fig. 14 is shown with a single winding with three taps it is an obvious alternative to provide two separate windings, e.g. of bifilar type, one with a single centre tap for curve A output, and one with three taps for curve B output, if separation of the two outputs is required for signal processing convenience.

Fig. 16 shows how such a sensor might be incorporated within a fluid-power cylinder assembly to give full-stroke signalling of piston rod position. The assembly has a cylinder 113 with end walls 114,116, and a piston 118 with a rod 120 that projects slidably through an aperture in one end wall 116. A hole 109 through the piston into the rod accommodates the sensor element 110, which is terminated in a suitably sealed bush lll in the cylinder head 114, the windings also being fully sealed and encapsulated to withstand the fluid and pressure within the cylinder 112. If required to maintain consistent screening effect through piston and rod, the hole can be sleeved with a good screening material such as brass tube 112.

The result is a much neater and simpler installation than afforded typically by external coupling of a convention sensor of LVDT or resistive type 122.

Another possible method of deriving a position signal from such a sensor is by connecting the complete tubular winding in series with a separate external fixed impedance Z_x to an a.c-.supply, as depicted in Fig. 17. The voltage at a tap T₂ connected between the fixed and variable impedances will then vary with travel of the sensor sleeve, to produce a single nominally linear analogue output as shown in Fig. 18 over the full traverse of the winding. If required, a duplicate winding can be provided, connected in series with a second fixed impedance Z₂, but arranged so that its output falls as the first output rises, as indicated by the broken lines in Figs. 17 and 18, to give two discrete output signals at any position.

In a variant of the Fig. 17 embodiment, (Fig. 19) the wound core 107 may be arranged to form the variable inductive element of an oscillator 122 in conjunction with external capacitor 124. Means C,M would then be provided to detect the change in resonant frequency as a measure of position.

Note that, in any embodiment, the linear sensor design may be inverted if required to have an external 21 tubular coil, and internal moving element of screening or ferromagnetic nature, of corresponding length to the coil. Fig. 20 shows schematically how such an embodiment might be incorporated to provide position feedback for a pneumatic diaphragm-operated control valve 130. A metal rod 125 is directly coupled to the actuator spindle 132 of the valve, and varies the relative inductances of coils 126 in a housing extension 127, to give output data corresponding to the full travel of the valve, using the techniques already described. This arrangement offers a mechanical design option to that exemplified by the Fig. 15 illustration in which a hole is required in the moving rod. Both may be equally well applied to various applications involving linear travel.

Claims

1. An inductive displacement sensor comprising an array of progressively wound coils (1-10; 61) extending along a path, and an inductance anomaly element (20;62) displaceable along the path and being dimensioned so as to affect the inductance of only a part of the coil array at any one time; the progressive nature of the coil array having the effect that the amount of the increase or decrease in inductance of the affected part varies in magnitude with the location of the affected part along the array.

2. A sensor according to claim 6 wherein the sensor comprises an array of unequal coils connected in series, and an inductance anomaly element displaceable relative to the array of coils and dimensioned so that at any one time it principally affects the inductance of only a subset of coils to which it is at that time adjacent, the inequality of the coils being such that the inductance of the whole array is different depending on which subset is affected.

3. A sensor according to claim 2 wherein the inductance anomaly element and the coils are dimensioned and arranged so that the element is locatable adjacent any single one of the coils so as to affect substantially the inductance of only that coil.

4. A sensor according to any preceding claim having an array of equal coils which are each divided into first and second sub-coils, the first sub-coils being mutually unequal and being serially connected to constitute a first array of unequal coils; the second sub-coils correspondingly being mutually unequal and also being serially connected to form a second said array.

5. A sensor according to claim 9 wherein the first array is in series with the second array and means are provided for monitoring the voltage drop across one array.

6. A sensor according to claim 9 or claim 10 wherein all of the first sub-coils are homopolar with the corresponding second sub-coils.

7. A sensor according to any of claims 6-11 wherein the coils are arranged as salient poles, their axes intersecting the intended relative displacement path of the inductance anomaly element .

8. A sensor according to claim 7 which includes a ferromagnetic core member of C-section, having two arms confronting each other across a gap, one arm being divided into core portions on which the coils are wound, the arrangement being such that the coil axes extend across the gap towards the other arm so that a flux circuit for each coil can extend around the C-section and across the gap.

9. A sensor according to claim 8 wherein the displacement path extends within the gap.

10. A sensor according to any of claims 1 to 6 wherein an array of progressively wound coils comprises a single flat coil wound as a single elongate eccentric spiral, elongate in the path, direction, and eccentric so that there is a high turn density at one end region, progressively decreasing towards the other end region.

11. A sensor according to claim 10 having a pair of such flat coils placed together in opposite orientations and connected in series.

12. A sensor according to any of claims 6 to 16 wherein the element is ferromagnetic (thus increasing inductance) or screening (i.e. a non-ferromagnetic conductor) (thus decreasing inductance) .

13. A sensor according to any of claims 1 to 11 wherein the inductance anomaly element is constituted by a gap in a relatively -large (ferromagnetic or screening) member which affects the inductance of every coil (or part) except for a part or subset adjacent a gap in the member.

14. A displacement sensor having a first elongate element having a wound portion and a second elongate element comprising electrically conductive and/or ferromagnetic material and of length substantially equal to the wound portion, said elements being relatively displaceable in their direction of elongation to vary the proportion of the wound portion which is adjacent the second element.

15. A sensor according to claim 14 wherein the range of displacement is substantially equal to the length of the wound portion, from a first configuration in which the wound portion and the second element are substantially in register to a second configuration in which they are substantially out of register.

16. A sensor according to claim 14 or claim 15 wherein either the wound portion or the second element is tubular and the other one of them is displaceable with the tube .

17. A sensor according to any of claims 14 to 16 wherein the wound portion comprises a plurality of coil portions with taps between them.

18. A sensor according to any of claims 14 to 16 including a fixed impedance connected in series with said wound portion; means for applying an AC supply across said fixed impedance and wound portion; and means for monitoring the voltage at a tap between said fixed impedance and said wound portion.